PRECALC 101 1.8.6 Test (TST): Functions Test Precalculus Sem 1 Points Possible:100. Score 100%

PRECALC 101 1.8.6 Test (TST): Functions Test Precalculus Sem 1 Points Possible:100 Date: 12.9.21 Answer the following questions using what you've learned from this unit. Write your responses in the space provided. ...

PRECALC 101 1.8.6 Test (TST): Functions Test Precalculus Sem 1 Points Possible:100 Date: 12.9.21 Answer the following questions using what you've learned from this unit. Write your responses in the space provided. 1. Find the equation of the line that is modeled by the values in the table shown below. Part I: Determine the slope of the line. Show the work you did to find the slope. (6 points) Slope intercept= y= 5/2x-4 y2-y1/x2-x1= (6-1)/(4-2)= 5/2=slope Part II: Using the slope you found in Part I and the values in the table, write the equation of the linear function represented by the table. Write your equation in point-slope form. (6 points) y-y1= m(x-x1)= y-1= 5/2(x-2) 2. For each function shown, answer the questions.Part I: Given the function , A. What restriction is there on the value under the square root symbol? In other words, what can't you do with a square root expression? (2 points) The square root isn’t allowed to be a negative so that means x has to be more than or equal to 2. B. What is the domain of this function? (2 points) (2, infinity) or x ≥ 2 Part II: Given the arithmetic sequence 4, 7, 10, 13, ..., A. What is the common difference for this sequence? (2 points) The common difference is 3. B. Which of the following equations will generate this sequence? (2 points) Part III: For the system of equations shown below,A. What are the two slopes of these equations? (2 points) The first slope is 3. The second slope is -2 B. Based on the slopes of the equations, how many solutions does this system have? (2 points) The system only has one solution. 3. For , find: Part I: Substitute 3 in for x in the function to solve for (4 points) f(3)= 1/(3)^2-6= art II: Substitute h for x in the function to solve for . (4 points) f(h)= 1/h^2-3 4. For and , find: Part I: A. Find the expression for g(x). (2 points B. Substitute the value of g(x) into the function f(x) in place of x to find the value of Part II:A. Find f(6). (2 points) 1/(6-5)= 1/1= 1 B. Substitute the value you found in Part I into g(x) to find g(f(6)). (4 points) 1^2+2=3 5. For the sequence given by , answer the following: Part I: Find the first 4 terms of the sequence by substituting n = 1, 2, 3, and 4 into the equation. (4 points) a1 Part II: Identify the 1st term and the 10th term of the sequence. (2 points) First term: a1=4(1)+5=9, Tenth term: a10=4(10)+5= 45 Part III: Use the 1st and 10th terms to find the sum of the first 10 terms. (2 points) 10(9+45)/2= 270 6. Graph the area bounded by , , , and . Part I: Graph the lines x = 0 and x = 12 (1 point)Part II: Should the lines you graphed in Part I be solid or dashed? (1 point) dashed Part III: Shade the region that satisfies the inequalities and . Be sure you look closely at the inequality symbols to determine which side of each line to shade. (2 points)Part IV: Graph the line . (1 point) Part V: Use the inequality to determine whether the line should be solid or dashed and whether you should shade above or below the line you just graphed. Shadethe region that satisfies the inequality. (1 points) Part VI: Graph the line by finding the x- and y-intercepts and drawing the line that connects those two points. (1 points) Part VII: Use the inequality to determine whether the line should be solid or dashed and whether you should shade above or below the line you just graphed. Shadethe region that satisfies the inequality. (1 points) Part VIII: There should be one region that satisfies all of the inequalities in this problem. Identify this region by drawing the inequality lines and shading the region that satisfies all of the inequalities. (2 points)7. For the function defined by: Part I: Evaluate . A. Identify the function that will be used when x = 0. (1 point) The function that will be used when x = 0 is f (x) = x2B. Find the value of this function when x = Part II: Graph . A. Graph the first function completely. (1 point) B. On the same graph you used to answer part (A), graph the second function completely. (1 point) C. Identify the value of x at which the functions change. Remove the parts of each line that are not included in domain of the corresponding function. (2 points) Value of x = 1D. Place open and closed circles appropriately on the ends of each line to complete the function. (2 points) n/a 8. Solve the following system of equations algebraically. Part I: Multiply one of the equations by a constant in order to solve by elimination. Show the new system of equations below. (2 points) Part II: Combine the two equations to eliminate one of the variables. Show the result of this combination below. (2 point Part III: Solve for the variable. What is this value? (2 points) Part IV: Substitute this value back into an equation to solve for the other variable. Write the solution to this system below. (4 points) Equation 1 : 3(2) – y = 0 y=6, Solution= (2, 6) 9. Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why. Part I A. Is the operation possible? Yes/no (2 points) yesB. What is the value of 3A? (2 points) 3*3 C. What is the value of 3A + B? (2 points) Part II: CA A. Is the operation possible? Yes/no (2 points) No B. What is the answer to CA? (2 points) 7 34 50.9 10. Express the following function, F(x), as a composition of two functions, f and g: . Part I: Find g(x) by identifying the function you are taking the square root of. (4 points) Part II: Find f(x) by identifying what you are doing to the function you found in Part I. What function is f(x)? (4 points) ƒ(x) = h(g(x)) Part III: Verify that . (2 points)It checks out.