Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. If , find .
2. Solv
...
Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. If , find .
2. Solve each equation for x.
(a) (b)
3. Simplify the expression.
4. Fill in the blanks.
Let , where .
__________ __________
5. Determine whether f is even, odd, or neither.
6. Find the range of the function.Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
7. The graphs of and are given.
a) For what values of is ?
b) Find the values of and .
8. A spherical balloon with radius inches has volume
.
Find a function that represents the amount of air required to inflate the balloon from a radius of
inches to a radius of inches.
9. It makes sense that the larger the area of a region, the larger the number of species that inhabit the
region. Many ecologists have modeled the species-area relation with a power function and, in
particular, the number of species S of bats living in caves in central Mexico has been related to the
surface area A measured in of the caves by the equation
(a) The cave called mission impossible near puebla, mexico, has suface area of .
How many species of bats would expect to find in that cave?
(b) If you discover that species of bats live in cave estimate the area of the cave.Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
10. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
Complete the table and find the slope.
11. Plot the graph of the function in (a) the standard viewing window and (b) the indicated window.
f (x) = x , [-3, 3] [-5, 5]
12. Plot the graph of the function f in an appropriate viewing window.
f (x) = 2x – 5x + 4x + 27
13. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
= 0.3 – 1.1x – 3.5; = –0.2 + 0.4x + 6.9
14. Determine whether f is one-to-one.
x
yStewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
15. If f (x) =
find f (–4), f (0), and f (1).
16. Refer to the graph of the function f in the following figure.
f (x)
–4 –3 –2 –1 1 2 3 4 5 6 7 8 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a. Find f (3).
b. Find the value of x for which (i) and (ii) .
c. Find the domain and range of f.
17. Let and . Find .
18. Find if
19. Let and . Find .
20. Find the function such that .
andStewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2. ,
3.
4.
5. even
6.
7. a) –2, 10
b) ,
8.
9. a) species
b)
10. ; slope =Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
11. a.
–10 10 x
10
–10
y
b.
–3 3 x
5
–5
y
12.
–4 –3 –2 –1 1 2 3 4 x
20
40
60
80
100
120
140
–20
y
13. (–3.30104, 3.40021), (6.30104, 1.47979)Stewart - Calculus 8e ET Chapter 1 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
14. Yes
15. f (–4) = 19, f (0) = 3, f (1) = 1.
16. a. 0
b. (i) 4 (ii) 3, 5
c. D: [3, 6], R: [–3, 1]
17. 37
18.
19. –6
20.Stewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Find all solutions of the equation correct to two decimal places.
2. Solve each equation for x.
(a) (b)
3. Find the exact value of the expression.
4. Find the range of the function.
5. Express the function in the form of .
6. Plot the graph of the function f in an appropriate viewing window.
f (x) = 5x – 3x + 3x – x + 26
7. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
= 0.3 – 1.2x – 3.4; = –0.2 + 0.2x + 6.3Stewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
8. Determine whether f is one-to-one.
x
y
9. The graph of f is given. Sketch the graph of on the same set of axes.
y = f x ( )
0.5 1 x
0.5
1
y
2
10. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
f(x) = ,
11. If f (x) =
find f (–1), f (0), and f (1).Stewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12. Refer to the graph of the function f in the following figure.
f (x)
–4 –3 –2 –1 1 2 3 4 5 6 7 8 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a. Find f (0).
b. Find the value of x for which (i) and (ii) .
c. Find the domain and range of f.
13. Determine whether the function is even, odd, or neither.
14. The following figure shows a portion of the graph of a function f defined on the interval .
Sketch the complete graph of f if it is known f is odd.
–1 1 x
1
–1
yStewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
15. By cutting away identical squares from each corner of a rectangular piece of cardboard and folding
up the resulting flaps, an open box can be made. If the cardboard is 13 in. long and 9 in. wide and
the square cutaways have dimensions of x in. by x in., find a function that gives the volume of the
resulting box.
9
13
x x
x x
x x
x x
13 – 2x
9 – 2x
16. Use the vertical line test to determine whether the curve is the graph of a function of x.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
17. Let and . Find .
18. Find if
19. Let and . Find .Stewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
20. Find the function such that .
andStewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. 1.75
2. ,
3.
4.
5.
6.
–4 –3 –2 –1 1 2 3 4 x
20
40
60
80
100
120
140
–20
y
7. (–3.22169, 3.57981), (6.02169, 0.25219)
8. No
9.
y = f x ( )
y = f –1 ( ) x
x
yStewart - Calculus 8e ET Chapter 1 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
10.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
11. f (–1) = 9, f (0) = 8, f (1) = 1.
12. a. 0
b. (i) 1 (ii) 0, 2
c. D: [0, 3], R: [–3, 1]
13. Neither
14.
–1 1 x
1
–1
y
15.
16. Yes
17. 65
18.
19. 70
20.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places.
f (x) = 0.5 – 1.8 + 2.2x – 4; = 2.8x – 4.3
a. (–0.55126, –5.84352),
(3.87001, 6.53604)
b. (–0.55126, –1.54352)
(0.28124, 10.83604)
(3.87001, 0.78748)
c. (–0.55126, –1.54352)
(3.87001, 0.78748)
d. (–0.55126, –5.84352),
(0.28124, –3.51252)
(3.87001, 6.53604)
____ 2. Starting with the graph of , find the equation of the graph that results from reflecting about
the line .
a.
b.
c.
d.
e.
____ 3. Use the Law of Exponents to rewrite and simplify the expression.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 4. Starting with the graph of , write the equation of the graph that results from shifting 5 units
right.
a.
b.
c.
d.
e.
____ 5. Suppose that the graph of is drawn on a coordinate grid where the unit of measurement
is an inch. How many miles to the right of the origin do we have to move before the height of the
curve reaches 2 ft? Rounded to the nearest mile.
a. 754.9 mi
b. 4,457,536.9 mi
c. 53,490,543 mi
d. 53,490,442.5 mi
e. 53,490,343 mi
____ 6. Find the exact value of the given expression.
tan–1 1
a.
b.
c.
d. 4Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Use the laws of logarithms to expand the expression.
ln
a.
ln [(x + 5)(x – 6)]
b.
ln (x + 5) – ln (x – 6)
c.
ln
d.
ln
____ 8. Simplify the expression.
a. 9
b. 18
c. 216
d. 729
____ 9. Find a formula for the inverse of the function.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 10. Find the exact value of the expression.
a. 7
b. 8
c. 6
d. 4
e. 5
____ 11. The graphs of and are given. For what values of x is ?
a. 4, 2
b. 0
c.
d.
e. –4, 12
____ 12. Which of the following graphs is neither even nor odd?
a.
b.
c.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 13. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides.
a.
b.
c.
d.
e.
____ 14. What is the equation of this graph?
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 15. Find the domain.
a.
b.
c.
d.
e.
____ 16. Find the range of the function.
a.
b.
c.
d.
e.
____ 17. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
What is the F-intercept and what does it represent?
a.
, Fahrenheit temperature corresponding to
b.
, Celsius temperature corresponding to
c. 32, Celsius temperature corresponding to
d. 0, Fahrenheit temperature corresponding to
e. 32, Fahrenheit temperature corresponding toStewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. If and , find a function g such that .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 19. The graph of the function follows. Choose the graph of
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
a.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
c.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
b.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
d.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
yStewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 20. Which of the following graphs is the graph of the function?
Graph 1
–2 –1 1 2
Graph 2
–4 –3 –2 –1 1 2 3 4
Graph 3
–4 –3 –2 –1 1 2 3 4
a. Graph 2
b. Graph 1
c. Graph 3Stewart - Calculus 8e ET Chapter 1 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. D
2. B
3. A
4. C
5. B
6. B
7. B
8. C
9. A
10. D
11. E
12. B
13. A
14. E
15. D
16. E
17. E
18. D
19. D
20. AStewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Find all solutions of the equation correct to two decimal places.
a.
b. ,
c. , ,
d. ,
e. ,
____ 2. Use the Law of Exponents to rewrite and simplify the expression.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 3. Starting with the graph of , write the equation of the graph that results from shifting 3 units
right.
a.
b.
c.
d.
e.
____ 4. Find the inverse function of .
a.
b.
c.
d.
e.
____ 5. Find (a) for the function f and the real number a.
;
a. 2
b. 1
c. 3
d. 0Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 6. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
,
a.
,
f = f –1
1 2 3 4 5 x
5 4 3 2 1
y
c.
,
f = f –1
1 2 3 4 5 x
1
–1
–2
–3
–4
–5
–6
–7
y
b.
,
f
f –1
1 2 3 4 5 6 7 8 x
1
–1
–2
–3
–4
–5
–6
–7
y
d.
,
f
f –1
1 2 3 4 5 6 7 8 x
8 7 6 5 4 3 2 1
yStewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Find the exact value of the given expression.
sin
a.
b. 0
c.
d. 1
____ 8. Simplify the expression.
a. 12
b. 36
c. 8
d. 64
____ 9. A box with an open top is to be constructed from a rectangular piece of card board with
dimensions in. by in. by cutting out equal squares of side at each corner and then
folding up the sides as in the figure.
Express the volume of the box as a function of .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 10. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides.
a.
b.
c.
d.
e.
____ 11. If , find and simplify , where .
a.
b.
c.
d.Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 12. Find the domain and sketch the graph of the function. What is its range?
f (x) =
a. D: (– , ); R: (– , 0] (8, )
–1 1 2 3 4 5 6 7 8 9 x
4 3 2 1
–1
–2
–3
–4
–5
–6
y
c. D: (– , ); R: (– , )
–2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4 3 2 1
–1
y
b. D: (– , ); R: [0, )
1 2 3 4 5 6 7 8 9 10 x
9 8 7 6 5 4 3 2 1
10
y
d. D: (– , ); R: [–1, )
–2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4 3 2 1
–1
yStewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 13. The graph of the function is given. State the value of .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 14. What is the equation of this graph?
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a.
b.
c.
d.
e.
____ 15. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
What is the F-intercept and what does it represent?
a.
, Fahrenheit temperature corresponding to
b.
, Celsius temperature corresponding to
c. 32, Celsius temperature corresponding to
d. 0, Fahrenheit temperature corresponding to
e. 32, Fahrenheit temperature corresponding toStewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 16. Graph the function by hand, not by plotting points, but by starting with the graph of one of the
standard functions and then applying the appropriate transformations.
a.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
b.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y d.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
____ 17. Suppose that the graph of is given f is given. Describe how the graph of the function
can be obtained from the graph of f.
a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the right and 3 units up.
c. Shift the graph 3 units to the left and 3 units down.
d. Shift the graph 3 units to the left and 3 units up.
e. None of theseStewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. Which of the following graphs is the graph of the function?
Graph 1
–2 –1 1 2
Graph 2
–4 –3 –2 –1 1 2 3 4
Graph 3
–4 –3 –2 –1 1 2 3 4
a. Graph 3
b. Graph 1
c. Graph 2Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 19. Find the function and its domain if and .
a.
b.
c.
d.
____ 20. The graph of the function has been compressed horizontally by a factor of 2.
Find the function for the transformed graph.
a.
b.
c.
d.Stewart - Calculus 8e ET Chapter 1 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2. B
3. E
4. E
5. B
6. A
7. C
8. B
9. C
10. D
11. D
12. C
13. D
14. C
15. E
16. B
17. A
18. C
19. A
20. AStewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with which to
enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that
gives the area of the garden. Select the correct answer.
x
y
a.
b.
c.
d.
2. An open rectangular box with volume has a square base. Express the surface area of the box
as a function of the length of a side of the base.
____ 3. Determine whether f is even, odd, or neither. Select the correct answer.
a. neither
b. odd
c. even
4. The monthly cost of driving a car depends on the number of miles driven. Julia found that in
October it cost her to drive mi and in July it cost her to drive mi. Express
the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a
suitable model.
5. If and , find a function g such that .Stewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 6. The graph of the function follows. Choose the graph of
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
a.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
c.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
b.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
d.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
yStewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
7. Sketch the graph of over one period.
8. Find the function and its domain if and .
____ 9. If a ball is thrown into the air with a velocity of , its height (in feet) after t seconds is given
by
.
Find the velocity when Select the correct answer.
a. ft/s
b. ft/s
c. ft/s
d. ft/s
e. ft/s
10. The position of a car is given by the values in the following table.
(seconds) 0 1 2 3 4
(meters) 0 21.9 25.8 69.2 92.2
Find the average velocity for the time period beginning when and lasting 2 seconds.
____ 11. Find the value of . Select the correct answer.
.
a.
b.
c.
d.
e.
12. Find the vertical asymptotes of the function.Stewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
13. Find the limit .
____ 14. Find the limit , if it exists. Select the correct answer.
a. 1
b. 3
c. 2
d. Does not exist
15. Evaluate the limit, if it exists.
16. Find the limit.
17. Determine where f is discontinuous.
____ 18. If f and g are continuous functions with
Select the correct answer.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19. How would you define in order to make f continuous at ?
____ 20. Use the graph to determine where the function is discontinuous. Select the correct answer.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a. At 0
b. On the interval
c. At
d. At 1Stewart - Calculus 8e ET Chapter 1 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. B
2.
3. C
4.
5.
6. D
7.
–2 –1 1 2 3 4 5 6 7 8 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
8.
9. B
10. 33.2 ft/s
11. A
12. none of these
13. –7
14. B
15.
16.
17.
18. E
19.
20. CStewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Plot the graph of the function f in an appropriate viewing window. Select the correct answer.
a.
–4 –3 –2 –1 1 2 3 4 x
3 2 1
–1
y
c.
–4 –3 –2 –1 1 2 3 4 x
3 2 1
–1
y
b.
–5 5 x
5
–5
y
d.
–5 5 x
5
–5
y
2. Plot the graph of the function f in an appropriate viewing window.Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
3. Use the Law of Exponents to rewrite and simplify the expression.
____ 4. Starting with the graph of , find the equation of the graph that results from reflecting about
the line . Select the correct answer.
a.
b.
c.
d.
e.
5. Use the Law of Exponents to rewrite and simplify the expression.
____ 6. Starting with the graph of , write the equation of the graph that results from shifting 5 units
right. Select the correct answer.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Find the inverse of f. Then sketch the graphs of f and on the same set of axes.
Select the correct answer.
,
a.
,
f = f –1
1 2 3 4 5 x
1
–1
–2
–3
–4
–5
–6
–7
y
c.
,
f
f –1
1 2 3 4 5 6 7 8 x
1
–1
–2
–3
–4
–5
–6
–7
y
b.
,
f
f –1
1 2 3 4 5 6 7 8 x
8 7 6 5 4 3 2 1
y
d.
,
f = f –1
1 2 3 4 5 x
5 4 3 2 1
y
8. Solve the equation.Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
9. When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor,
which stores electric charge given by
(The maximum charge capacity is and t is measured in seconds.) How long does it take to
recharge the capacitor to 90% of capacity if ?
____ 10. If , evaluate the difference quotient . Select the correct answer.
a.
b.
c.
d. h
e. none of these
11. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides.
12. The graph shown gives the weight of a certain person as a function of age. Find the age at which
the person started an exercise program.Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
13. What is the equation of this graph?
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
14. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear
function.
What is the F-intercept and what does it represent?
____ 15. Classify the function as a Polynomial function, a Rational function, an algebraic function, or other.
Select the correct answer.
a. Other
b. Algebraic
c. Rational
d. Polynomial
16. Use the table to evaluate the expression .
1 2 3 4 5 6
3 2 1 0 1 2
6 5 2 3 4 6
17. What is , given that and ?Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. Which of the following is the equation for the function ? Select the correct answer.
a.
b.
c.
d.
e.
19. Find the function and its domain if and .
20. The graph of the function has been stretched horizontally by a factor of 2.
Find the function for the transformed graph.Stewart - Calculus 8e ET Chapter 1 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2.
–0.3 0.3 x
0.3
–0.3
y
3.
4. B
5.
6. C
7. D
8. x = ln 1
2 – 5
9. seconds
10. E
11.
12.
13.
14. 32, Fahrenheit temperature corresponding to
15. C
16. 2
17. f(x)
18. D
19.
20.Stewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Plot the graph of the function f in an appropriate viewing window.
2. Plot the graph of the function f in an appropriate viewing window.
____ 3. Starting with the graph of , find the equation of the graph that results from reflecting about
the line . Select the correct answer.
a.
b.
c.
d.
e.
4. Use the Law of Exponents to rewrite and simplify the expression.
____ 5. If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of
bacteria after t hours is
.
When will the population reach 55,000? Round the answer to the nearest tenth.
Select the correct answer.
a. 22.3 hours
b. 27.3 hours
c. 32.3 hours
d. 37.3 hours
e. 17.3 hoursStewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 6. Find (a) for the function f and the real number a. Select the correct answer.
;
a. –2
b. –1
c. 1
d. 0
7. Find the exact value of the given expression.
sin–1 1
2
8. Use the laws of logarithms to expand the expression.
ln
____ 9. Simplify the expression. Select the correct answer.
a. 25
b. 32
c. 7
d. 10
10. If , evaluate the difference quotient .
____ 11. A rectangle has perimeter m. Express the area of the rectangle as a function of the length
of one of its sides. Select the correct answer.
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12. Find the domain of the function
____ 13. The graph shown gives the weight of a certain person as a function of age. Find the age at which
the person started an exercise program. Select the correct answer.
a. 20
b. 35
c. 54
d.
e. 38
14. An open rectangular box with volume has a square base. Express the surface area of the box
as a function of the length of a side of the base.
____ 15. Determine whether f is even, odd, or neither. Select the correct answer.
a. neither
b. even
c. odd
16. Find the range of the function.
17. If and , find a function g such that .Stewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. The graph of the function follows. Choose the graph of
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
a.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
c.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
b.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
y
d.
–9 –6 –3 3 6 9 x
9 6 3
–3
–6
–9
yStewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 19. Suppose that the graph of is given f is given. Describe how the graph of the function
can be obtained from the graph of f. Select the correct answer.
a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the right and 3 units up.
c. Shift the graph 3 units to the left and 3 units up.
d. Shift the graph 3 units to the left and 3 units down.
e. None of these
20. Which of the following graphs is the graph of the function?
Graph 1
–2 –1 1 2
Graph 2
–4 –3 –2 –1 1 2 3 4
Graph 3
–4 –3 –2 –1 1 2 3 4Stewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
–4 –3 –2 –1 1 2 3 4 x
3 2 1
–1
y
2.
–0.3 0.3 x
0.3
–0.3
y
3. D
4.
5. B
6. B
7.
8. ln (x + 4) – ln (x – 5)
9. A
10. none of these
11. C
12.
13. DStewart - Calculus 8e ET Chapter 1 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
14.
15. B
16.
17.
18. C
19. A
20. Graph 2Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Plot the graph of the function f in an appropriate viewing window.
____ 2. Find the points of intersection of the graphs of the functions. Express your answers accurate to five
decimal places. Select the correct answer.
f (x) = 0.5 – 1.8 + 2.2x – 4; = 2.8x – 4.3
a. (–0.55126, –5.84352),
(3.87001, 6.53604)
b. (–0.55126, –1.54352)
(0.28124, 10.83604)
(3.87001, 0.78748)
c. (–0.55126, –1.54352)
(3.87001, 0.78748)
d. (–0.55126, –5.84352),
(0.28124, –3.51252)
(3.87001, 6.53604)
3. The function is graphed below.
–10 –7.5 –5 –2.5 2.5 5 7.5 10 x
2.5
5
7.5
10
12.5
15
–2.5
–5
–7.5
–10
y
4. Find the inverse function of .Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 5. Determine whether the function is one-to-one.
a. Yes
b. No
6. Find the exact value of the given expression.
tan–1 1
7. Use the laws of logarithms to expand the expression.
ln
____ 8. Simplify the expression. Select the correct answer.
a. 9
b. 18
c. 216
d. 729
9. Solve the equation.
10. A box with an open top is to be constructed from a rectangular piece of card board with
dimensions in. by in. by cutting out equal squares of side at each corner and then
folding up the sides as in the figure.
Express the volume of the box as a function of .Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 11. Find an expression for the function whose graph is the bottom half of the parabola
. Select the correct answer.
a.
b.
c.
d.
e.
12. Find the domain of the function.
13. Find the domain and sketch the graph of the function. What is its range?
f (x) =
____ 14. The graph shown gives the weight of a certain person as a function of age. Find the age at which
the person started an exercise program. Select the correct answer.
a. 20
b. 54
c. 38
d.
e. 35Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 15. Find the domain. Select the correct answer.
a.
b.
c.
d.
e.
16. Graph the function by hand, not by plotting points, but by starting with the graph of one of the
standard functions and then applying the appropriate transformations.Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 17. The graph of the function follows. Choose the graph of
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
b.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y d.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
yStewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
18. Sketch the graph of over one period.
19. Find the function and its domain if and .
____ 20. The graph of the function has been stretched horizontally by a factor of 2.
Find the function for the transformed graph. Select the correct answer.
a.
b.
c.
d.Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
–4 –3 –2 –1 1 2 3 4 x
3 2 1
–1
y
2. D
3.
4.
5. B
6.
7. ln (x + 5) – ln (x – 6)
8. C
9. x = ln 1
2 – 5
10.
11. A
12. (–
13. D: (– , ); R: (– , )Stewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
–2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4 3 2 1
–1
y
14. D
15. D
16.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
17. A
18.
–2 –1 1 2 3 4 5 6 7 8 x
5 4 3 2 1
–1
–2
–3
–4
–5
yStewart - Calculus 8e ET Chapter 1 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19.
20. C
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