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GACE Middle Grades Math: Properties of Functions Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

Page 1

Question 1 1.

Use f(x) and g(x) to find f(x) * g(x).

f(x) = -x + 5 and g(x) = 3x + 2

Question 2 2.

Find the domain of the inverse function of:

f(x) = 1/(x-3)

Question 3 3. Which one of these functions has a domain of all real numbers?

Question 4 4. Which of the following is the inverse function of f(x) = 3x?

Question 5 5. The amount of money you spend on coffees every month can be calculated as a function of the number of drinks you order every month. What are the independent and dependent variables in this function?

Page 2

Question 6 6. If the domain of the function f(x) = x^2 is 0 ≤ x, what is the range of f?

Question 7 7. What notation do you use to show that you have an inverse function?

Question 8 8. The revenue of a company is represented by R(x) and their costs are represented by C(x). What is the profit function R(x) - C(x)?

Question 9 9. If f(x) = 5 - 2x and g(x) = -4x + 2, find g(f(x)).

Question 10 10. When the graph of f(x - 1) + 3 is changed into the graph of f(x + 1) + 3, the graph will shift in which direction?

Page 3

Question 11 11. Which of the following is the inverse function of f(x) = 2x - 3?

Question 12 12. Which function would NOT pass the horizontal line test?

Question 13 13.

What is the composite of the function below and its inverse?

f(x) = (x-2)/3

f^(-1)(x) = 3x + 2

Note: f^(-1)(x) indicates the inverse of the function f.

Question 14 14. Use the information given to find h(x) / l(x): h(x) = 6x2 and l(x) = 2x5

Question 15 15.

Use f(x) and g(x) to find g(x) - f(x).

Here, f(x) = -x + 5 and g(x) = 3x + 2.

Page 4

Question 16 16. In the figure shown below, the graph of the yellow function is a translation of the graph of the blue function. If the expression for the blue function is y(x) = b(x), which of the following is the equation of the yellow function?

Question 17 17. What is the range of the function: g(x) = |x| + 1

Question 18 18. If f(x) = 5 + 3x and g(x) = 5 - 9x, find f(g(2)).

Question 19 19.

Find the domain of f(g(x)), if:

f(x) = 1/x

g(x) = 1/(x+4)

Question 20 20.

Find f(g(2)) if:

f(x) = x^2

g(x) = x^3

Page 5

Question 21 21. What is the domain of the function below?

Question 22 22. If f(x) = -2x - 5 and g(x) = x^2 + 1, find f(f(x)).

Question 23 23.

Find the inverse function of:

y = 1/x

Question 24 24. How do you determine whether a function is an inverse of another function?

Question 25 25. Evaluate f(x) = √(x), when x = 9.

Page 6

Question 26 26.

Find the inverse of the following function:

f(x) = 2x + 1

Question 27 27. Which kind of transformation stretches or shrinks the graph of the function?

Question 28 28. Recalling function notation, we want x to be w. Therefore, if f(x) = (3x + 5) / 2, find f(w).

Question 29 29. Evaluate h(x) = 5x + 1, when x=3.

Question 30 30. Find the domain of f(x)/g(x), if:

GACE Middle Grades Math: Properties of Functions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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