Question 1

Given the equation of a line $2x - 3y = 6$, what is the equation of a line perpendicular to it that passes through the point $(1, -2)$? Leave your answer in general form.

Accepted Answer

$3x + 2y = -1$

Question 2

Find the equation of the line that passes through the points $(2, 5)$ and $(4, 9)$. Express your answer in slope-intercept form.

Accepted Answer

$y = 2x + 1$

Question 3

If the average rate of change of a function $f(x)$ from $x = 1$ to $x = 4$ is $5$, which of the following could be the value of $f(4)$ if $f(1) = 2$?

Accepted Answer

$f(4) = 17$

Question 4

A graph of $y = f(x)$ is provided. If you apply the transformation $g(x) = f(x-2) + 3$, what happens to the graph?

Accepted Answer

It shifts right by 2 units and up by 3 units.

Question 5

Find the domain of the function $f(x) = \dfrac{1}{x^2 - 9}$.

Accepted Answer

$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$

Question 6

Which of the following is the parent function for a quadratic equation?

Accepted Answer

$f(x) = x^2$

Question 7

Given $f(x) = 2x + 1$ and $g(x) = x^2$, find $(f + g)(3)$.

Accepted Answer

$16$

Question 8

If $f(x) = x^3$ and $g(x) = x + 2$, what is $(f \circ g)(1)$?

Accepted Answer

$27$

Question 9

Which of the following functions has an inverse that is also a function?

Accepted Answer

$f(x) = 3x + 2$

Question 10

Given $f(x) = x^2$ and $g(x) = \sqrt{x}$, which pair of functions are inverses of each other for $x \geq 0$?

Accepted Answer

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

Question 11

Given the equation $y = 5x - 7$, what is the equation for its inverse?

Accepted Answer

$y = \dfrac{x + 7}{5}$

Question 12

If $f(x) = 2x - 3$, find $f^{-1}(x)$.

Accepted Answer

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

Question 13

Given $f(x) = x^2$ and $g(x) = x + 1$, find $(f \circ g)(2)$.

Accepted Answer

$9$

Question 14

Which of the following is the correct difference quotient for $f(x) = x^2$?

Accepted Answer

$\dfrac{(x+h)^2 - x^2}{h}$

Question 15

A medical researcher models the growth of bacteria with $N(t) = 100e^{0.5t}$. What is the population after 4 hours?

Accepted Answer

$N(4) = 100e^{2}$

Question 16

A chemical reaction rate is modeled by $R(t) = 5t^2 - 3t + 2$. What is the average rate of change from $t = 1$ to $t = 3$?

Accepted Answer

$16$

Question 17

Which of the following is NOT a function?

Accepted Answer

$y^2 = x$

Question 18

If $f(x) = 3x - 2$ and $g(x) = x^2$, find $(g \circ f)(2)$.

Accepted Answer

$16$

Question 19

A company’s profit $P(x)$ is modeled by $P(x) = -2x^2 + 40x - 100$, where $x$ is the number of units sold. What is the maximum profit?

Accepted Answer

$P(10) = 100$

College Algebra: Study Guide on Functions, Transformations, and Operations

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