Question 1

Which of the following statements correctly describes when a function $$f$$ has an inverse function $$f^{-1}$$?

Accepted Answer

A function has an inverse if and only if it is a one-to-one function.

Question 2

Given $$f(x) = 2x + 3$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-3}{2}$$

Question 3

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$ on $$(-\infty, \infty)$$

Question 4

If $$f(x) = ax + b$$ where $$a 
eq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-b}{a}$$

Question 5

Which of the following is the correct definition of a one-to-one function?

Accepted Answer

For all $$a$$ and $$b$$, if $$f(a) = f(b)$$ then $$a = b.$$

Question 6

Consider the function $$f(x) = x^2$ with domain $$[0, \infty)$$. What is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x}$$

Question 7

In the rectangular coordinate system, what are the coordinates of the origin?

Accepted Answer

$$(0, 0)$$

Question 8

Which quadrant does the point $$(-3, 4)$$ lie in?

Accepted Answer

Quadrant II

Question 9

If the graph of $$y = f(x) is $$symmetric about the y-axis, which of the following must be true?

Accepted Answer

Replacing $$x by$$ $$-x$$ yields an equivalent equation.

Question 10

Which of the following is the correct process to find the inverse of a one-to-one function $$f$$?

Accepted Answer

Solve $$y = f(x)$$ for $$x in $$terms of $$y$$, then replace $$y$$ with $$x.$$

Question 11

Which of the following equations represents a function that is symmetric about the origin?

Accepted Answer

$$y = x^3$

Question 12

If $$f(x) = x^2$ + 2x - 3$$, what are the $$x-$$intercepts of its graph?

Accepted Answer

$$x = -3$$ and $$x = 1$$

Question 13

Which of the following is NOT a property of the inverse function $$f^{-1}$$?

Accepted Answer

$$f^{-1} is $$always the same as $$\frac{1}{f}$$

Question 14

A function $$f is $$defined by $$f(x) = |x|. $$Which statement is true about its graph?

Accepted Answer

It is symmetric about the y-axis.

Question 15

Which of the following points is in Quadrant IV of the rectangular coordinate system?

Accepted Answer

$$(3, -2)$$

Question 16

If $$f(x) is a $$one-to-one function and $$g(x) is $$also one-to-one, what can be said about the composite function $$f \circ g$$?

Accepted Answer

$$f \circ g is $$also one-to-one.

Question 17

Which of the following is the correct way to check if a graph represents a function?

Accepted Answer

Use the vertical line test.

Question 18

If $$f(x) = x^2$ is restricted to the domain $$[0, \infty)$$, what is the range of f$?

Accepted Answer

$$[0, \infty)$$

Question 19

Which of the following is true about the graph of $$y = x^2$?

Accepted Answer

It is symmetric about the y-axis.

Functions, Inverses, and Graphs in Rectangular Coordinates

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