Question 1

Which of the following best describes the Vertical Line Test and its purpose?

Accepted Answer

It is used to check if a relation is a function by seeing if any vertical line crosses the graph more than once.

Question 2

What does the Horizontal Line Test determine about a function?

Accepted Answer

Whether the function is one-to-one (injective).

Question 3

Given the set of ordered pairs $$\{(7,7), (8,8), (9,4.5), (10,6.5)\}$$, is this a function and is it one-to-one?

Accepted Answer

It is a function and it is one-to-one.

Question 4

If a relation is a function, which value cannot repeat?

Accepted Answer

The x-values.

Question 5

If a function is one-to-one, which value cannot repeat?

Accepted Answer

The y-values.

Question 6

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

Accepted Answer

$$f(x) = x^2$

Question 7

Find the inverse of $$f(x) = 3x + 1.$$

Accepted Answer

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

Question 8

Given $$f(x) = (x+9)^3$, what is f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} - 9$$

Question 9

What is the domain and range of $$f(x) = x^3$ + 8$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 10

If $$f(x) = 4x + 1$$, what is the domain and range of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 11

Given the point $$(2,8) is on $$the graph of a one-to-one function $$f(x)$$, what point must be on the graph of $$f^{-1}(x$$)$$?

Accepted Answer

$$(8,2)$$

Question 12

If $$f(x)$$ and $$g(x)$$ are inverse functions, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 13

Find the inverse of $$f(x) = \frac{3}{x-4}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{3}{x} + 4$$

Question 14

Which of the following sets of ordered pairs is NOT a function?

Accepted Answer

$$\{(2,4), (5,9), (2,14), (6,9)\}$$

Question 15

Given $$f(x) = x^2$, which of the following statements is true?

Accepted Answer

It passes the Vertical Line Test but fails the Horizontal Line Test.

Question 16

If $$f(x) = -2x$$ and $$g(x) = -2x$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

No, because $$f(g(x)) 
eq x.$$

Question 17

A medical test result is modeled by $$f(x) = 4x + 1$$, where $$x is $$the concentration of a substance. If the test result is $$17$$, what is the concentration?

Accepted Answer

$$x = 4$$

Question 18

Suppose a chemical reaction rate is given by $$f(x) = x^3$ + 8$$, where $$x is $$the temperature. If the reaction rate is $$35$$, what is the temperature?

Accepted Answer

$$x = \sqrt[3]{27}$$

Question 19

If $$f(x) = x^3$ + 8$$ and $$g(x) = \sqrt[3]{x-8}$$, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Functions, One-to-One Functions, and Inverse Functions: Key Concepts and Applications

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