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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