Question 1

Which of the following best describes a function?

Accepted Answer

A rule that assigns each element of the domain to exactly one element of the range.

Question 2

Given the set of ordered pairs $\{(-5, -7), (-3, -2), (-1, 6), (0, -2), (3, 5), (5, -7)\}$, what is the domain?

Accepted Answer

$\{-5, -3, -1, 0, 3, 5\}$

Question 3

A thermometer reads $37^\circ$C. Using the formula $F = \frac{9}{5}C + 32$, what is the temperature in Fahrenheit?

Accepted Answer

$F = 98.6$

Question 4

Which of the following relationships is NOT a function?

Accepted Answer

Some inputs have more than one output.

Question 5

Given the function $f(x) = 2x^3 + 5x^2 - 28x - 15$, what is $f(2)$?

Accepted Answer

$f(2) = 45$

Question 6

A graph passes the vertical line test if:

Accepted Answer

No vertical line intersects the graph at more than one point.

Question 7

The function $V(t) = 3.77t^2 + 24.4t + 131.9$ models the value of the medical 3D printing market (in millions of dollars), where $t$ is the number of years after 2010. What is the projected value in 2027?

Accepted Answer

$V(17) = 1609.9$

Question 8

If a table lists the number of female physicians in the U.S. for each year from 2015 to 2040, is this relationship a function?

Accepted Answer

Yes, because each year corresponds to exactly one number of physicians.

Question 9

Given the function $g(t)$ representing the number of older men in the workforce (in millions) as a function of year $t$, if $g(2020) = 21$, what does this mean?

Accepted Answer

There were 21 million older men in the workforce in 2020.

Question 10

For the function $V(t) = 3.77t^2 + 24.4t + 131.9$, what value of $t$ corresponds to the year 2025?

Accepted Answer

$t = 15$

Question 11

Which of the following is the correct range for the function defined by the set $\{(-5, -7), (-3, -2), (-1, 6), (0, -2), (3, 5), (5, -7)\}$?

Accepted Answer

$\{-7, -2, 6, 5\}$

Question 12

If a graph continues indefinitely to the left and is bounded on the right at $x = 4$, what is the domain?

Accepted Answer

$(-\infty, 4]$

Question 13

Suppose $f(x) = -x^2 + 4x$. Is $y$ a function of $x$?

Accepted Answer

Yes, because each $x$ gives exactly one $y$ value.

Question 14

A scatter plot is useful for which of the following purposes?

Accepted Answer

Visualizing the relationship between two variables using ordered pairs.

Question 15

If $f(x) = 2x^3 + 5x^2 - 28x - 15$, what is $f(4)$?

Accepted Answer

$f(4) = 81$

Question 16

If the number of older men in the workforce is modeled by $g(t)$ and $g(2030) = 19.6$, what is the input and what is the output?

Accepted Answer

Input: 2030, Output: 19.6

Question 17

Which of the following statements about the domain and range of a function is correct?

Accepted Answer

The domain is the set of all possible input values, and the range is the set of all possible output values.

Question 18

If a function is defined by a table where each input year is listed only once, what can you conclude?

Accepted Answer

The relationship is a function.

Question 19

If the value of the medical 3D printing market in 2025 is projected to be $V(15) = 1319.9$ million dollars, what does this mean in context?

Accepted Answer

In 2025, the market is projected to be approximately $1.32$ billion dollars.

College Algebra: Functions, Graphs, and Models – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards