Q: Which of the following best describes the graph of $y = \sqrt{x}$?

Starts at $(0,0)$ and increases slowly to the right

Question 1

Given the points $A(2, -3)$ and $B(-4, 5)$, what is the distance between $A$ and $B$?

Accepted Answer

$10$

Question 2

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$\{(0,1), (1,2), (2,3)\}$

Question 3

If $f(x) = 2x^2 - 3x + 1$, what is $f(-2)$?

Accepted Answer

$19$

Question 4

Which of the following equations is in point-slope form for a line with slope $m = -3$ passing through $(2, 5)$?

Accepted Answer

$y - 5 = -3(x - 2)$

Question 5

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

Accepted Answer

$11$

Question 6

Which of the following describes the graph of $y = |x - 3| + 2$ compared to $y = |x|$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 7

What is the vertex of the quadratic function $f(x) = -2(x + 1)^2 + 5$?

Accepted Answer

$(-1, 5)$

Question 8

Which of the following functions is even?

Accepted Answer

$f(x) = x^2$

Question 9

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -4x^2 + 32x - 60$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $68$ at $x = 4$

Question 10

Which of the following is the domain of $f(x) = \sqrt{x - 5}$?

Accepted Answer

$x \geq 5$

Question 11

Given the function $f(x) = \frac{2x}{x-1}$, which value is NOT in the domain?

Accepted Answer

$x = 1$

Question 12

Which of the following describes the transformation from $y = x^2$ to $y = -3(x - 2)^2 + 4$?

Accepted Answer

Vertical stretch by 3, reflection over x-axis, right 2 units, up 4 units

Question 13

If $f(x) = x^2 - 4$ and $g(x) = x + 2$, what is $(f + g)(3)$?

Accepted Answer

$15$

Question 14

Which of the following is the equation of a horizontal line passing through $(4, -2)$?

Accepted Answer

$y = -2$

Question 15

Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ x^2 & x \geq 0 \end{cases}$, what is $f(-3) + f(2)$?

Accepted Answer

$7$

Question 16

Which of the following best describes the graph of $y = \sqrt{x}$?

Accepted Answer

Starts at $(0,0)$ and increases slowly to the right

Question 17

If $f(x)$ is an odd function and $f(3) = 7$, what is $f(-3)$?

Accepted Answer

$-7$

Question 18

A line passes through $(1, 2)$ and $(5, 10)$. What is its equation in slope-intercept form?

Question 19

Which of the following best describes the range of $f(x) = x^2 - 4$?

Accepted Answer

$y \geq -4$

College Algebra Study Notes: Graphs, Functions, and Linear & Quadratic Functions

Study Guide - Practice Questions

Study Guide - Flashcards