Chapter Practice Test on Functions
Chapter
Chapter 1
Section
Chapter Practice Test on Functions
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Solutions 11 Videos

Consider the graph of the relation shown.

a) Is the relation a function? Explain.

b) State the domain and range.

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Q1

Describe the transformations that must be applied to y = x^2 to obtain the function f(x) = -(x + 3)^2 - 5, then graph the function.

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Q5

Given the graph shown, describe the transformations that were performed to get this function. Write the algebraic representation, using function notation.

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Q6

(3, 5) is a point on the graph of y = f(x). Find the corresponding point on the graph of each of the following relations.

\displaystyle y = 3(-x + 1) + 2

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Q7a

(3, 5) is a point on the graph of y = f(x). Find the corresponding point on the graph of each of the following relations.

\displaystyle y = f^{-1}(x)

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Q7b

Find the inverse of f(x) = 2(x + 1).

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Q8

A certain tax policy states that the first $50 000 of income is taxed at 5% and any income above $50 000 is taxed at 12%.

a) Calculate the tax on \$125 000

b) Write a function that models the tax policy.

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Q9

a) Sketch the graph f(x) where f(x) = \displaystyle \begin{cases} &2^x, &\text{ if } x< 0\\ &\sqrt{x} + 3, &\text{ if } x\geq 0 \end{cases}

b) Is f(x) continuous over its entire domain? Explain.

c) State the intervals of increase and decrease.

d) State the domain and range of this function.

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Q10