Shifted right 3 units and up 2 units

Domain: $(-\infty, \infty)$, Range: $[-4, \infty)$

Reflected over the $x$-axis, vertically stretched by 2, shifted right 1 unit and up 3 units

Question 1

Which of the following points is a solution to the equation $3x - 2y = 6$?

Accepted Answer

$(2, 0)$

Question 2

Find the $x$- and $y$-intercepts of the line $3x + 2y = 12$.

Accepted Answer

$x$-intercept: $(4, 0)$, $y$-intercept: $(0, 6)$

Question 3

Given the endpoints of a diameter of a circle at $(2, -3)$ and $(6, 5)$, what is the length of the radius?

Accepted Answer

$\sqrt{17}$

Question 4

Find the equation of the circle with center at $(3, -2)$ and radius $5$.

Accepted Answer

$(x - 3)^2 + (y + 2)^2 = 25$

Question 5

Which of the following correspondences is NOT a function?

Accepted Answer

A relation where one $x$-value maps to two different $y$-values

Question 6

Find the domain of the function $f(x) = \sqrt{7 - x}$.

Accepted Answer

$(-\infty, 7]$

Question 7

Given the cost function $C = 20x + 20000$, how many items must be produced if costs reached $144,000$?

Accepted Answer

$6,200$

Question 8

Find the slope and $y$-intercept of the equation $2y - 4x = 8$.

Accepted Answer

Slope: $-2$, $y$-intercept: $4$

Question 9

Determine if the lines $y = 2x + 3$ and $2y - 4x = 8$ are parallel, perpendicular, or neither.

Accepted Answer

Parallel

Question 10

For the piecewise function $f(x) = \begin{cases} x + 2, & x < 1 \ 3x - 1, & x \geq 1 \end{cases}$, find $f(0)$.

Accepted Answer

$2$

Question 11

How is the graph of $f(x) = \sqrt{x}$ transformed to obtain $g(x) = \sqrt{x - 3} + 2$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 12

Find the domain and range of the function $f(x) = x^2 - 4$.

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[-4, \infty)$

Question 13

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

Accepted Answer

$1$

Question 14

Which of the following best describes the transformation from $y = x^2$ to $y = -2(x - 1)^2 + 3$?

Accepted Answer

Reflected over the $x$-axis, vertically stretched by 2, shifted right 1 unit and up 3 units

Question 15

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

Accepted Answer

$9$

Question 16

Which of the following intervals describes where the function $f(x) = -x^2 + 4$ is increasing?

Accepted Answer

$(-\infty, 0)$

Question 17

Given the equation $x^2 + y^2 = 49$, what is the center and radius of the circle?

Accepted Answer

Center: $(0, 0)$, Radius: $7$

Question 18

Which of the following equations represents a line perpendicular to $y = -\frac{1}{2}x + 3$?

Accepted Answer

$y = 2x - 1$

Question 19

Evaluate the difference quotient $\frac{f(x+h) - f(x)}{h}$ for $f(x) = x^2$.

Accepted Answer

$2x + h$

College Algebra Exam 1 Review: Study Notes and Key Concepts

Study Guide - Practice Questions