Question 1

Which of the following best describes a one-to-one function?

Accepted Answer

A function where each $$y$$ value is paired with exactly one $$x$$ value.

Question 2

Given the graph of $$f(x)$$ and $$g(x) in $$the first image, what is the value of $$(f \circ g)(-3)$$?

Accepted Answer

$$f(g(-3)) = f(2) = -2$$

Question 3

Which test can be used to determine if a function is one-to-one from its graph?

Accepted Answer

Horizontal Line Test

Question 4

If a function $$f(x)$$ passes the horizontal line test, what can be concluded?

Accepted Answer

The function is one-to-one and has an inverse.

Question 5

Given the graphs in the third image, which graph correctly shows a one-to-one function and its inverse?

Accepted Answer

Graph A

Question 6

Suppose $$f(x) is a $$one-to-one function. Which of the following statements is always true?

Accepted Answer

$$f(a) = f(b)$$ implies $$a = b$$

Question 7

Given $$f(x)$$ and $$g(x)$$ from the second image, what is $$(f \circ g)(1)$$?

Accepted Answer

$$f(g(1)) = f(0) = 2$$

Question 8

Which of the following is NOT a property of inverse functions?

Accepted Answer

$$f(x) + f$$^{-1}$$(x) = x$$

Question 9

A function $$f(x) is $$defined as $$f(x) = 2x + 3. $$What is its inverse $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 10

If $$f(x) is $$one-to-one and $$f(2) = 5$$, what is $$f^{-1}(5$$)$$?

Accepted Answer

$$2$$

Question 11

Which of the following real-world scenarios can be modeled by a one-to-one function?

Accepted Answer

Assigning each student a unique student ID number.

Question 12

If $$f(x) is a $$one-to-one function and $$f(a) = f(b)$$, what must be true?

Accepted Answer

$$a = b$$

Question 13

Given $$f(x)$$ and $$g(x)$$ from the first image, what is $$(f + g)(-2)$$?

Accepted Answer

$$f(-2) + g(-2) = 2 + 2 = 4$$

Question 14

Which of the following statements is true about the graph of a function and its inverse?

Accepted Answer

They are reflections of each other over the line $$y = x.$$

Precalculus Study Guide: Inverse and Composite Functions, One-to-One Functions, and Graph Interpretation

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