Q: Find the domain of the function $f(x) = \dfrac{3x - 2}{x^2 - 18}$.

All real numbers except $x = \sqrt{18}$ and $x = -\sqrt{18}$

Q: Find the domain and range of the function represented by the graph of $y = -x + 3$ for $x$ in $[0, 3]$.

Domain: $[0, 3]$, Range: $[0, 3]$

Question 1

Find the distance between the points $A = (5, 3)$ and $B = (7, 7)$. Give an exact answer, and where appropriate, an approximation to three decimal places.

Accepted Answer

$\sqrt{20}, 4.472$

Question 2

Which of the following is the equation of a circle with center at $(4, -2)$ and radius $5$?

Accepted Answer

$(x - 4)^2 + (y + 2)^2 = 25$

Question 3

Find the center and radius of the circle given by $x^2 + y^2 - 6x + 8y = 0$.

Accepted Answer

Center: $(3, -4)$, radius: $5$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$\{(1, 2), (2, 3), (1, 5)\}$

Question 5

Find the domain of the function $f(x) = \dfrac{4x}{x^2 - 16}$.

Accepted Answer

All real numbers except $x = 4$ and $x = -4$

Question 6

Given $f(x) = x^2 + 5x$, find $f(-3)$.

Accepted Answer

$-4$

Question 7

Find the slope of the line containing the points $(1, 4)$ and $(7, -4)$.

Accepted Answer

$-\dfrac{4}{3}$

Question 8

Find the slope and $y$-intercept of the equation $12x + 9y = 45$.

Accepted Answer

Slope: $-\dfrac{4}{3}$, $y$-intercept: $5$

Question 9

Write a slope-intercept equation for a line with slope $\dfrac{2}{3}$ passing through $(0, 5)$.

Accepted Answer

$y = \dfrac{2}{3}x + 5$

Question 10

Determine whether the pair of lines $8x - 6y = 6$ and $4x - 3y = 6$ are parallel, perpendicular, or neither.

Accepted Answer

Parallel

Question 11

Solve the equation $9x - (2x - 1) = 22$.

Accepted Answer

$x = \dfrac{11}{7}$

Question 12

Solve the inequality and graph the solution set: $|x + 2| < 9$.

Accepted Answer

$(-11, 7)$

Question 13

Given the relation $\{(-7, 6), (-7, -3), (0, 7), (8, -7), (8, 7)\}$, is this relation a function?

Accepted Answer

No

Question 14

Given $f(x) = 4x^2 + 2x$, find $f(3)$.

Accepted Answer

$42$

Question 15

Given $g(h) = 12h^2 + 28h - 3h^3$, find $g(2)$.

Accepted Answer

$29$

Question 16

Find the domain of the function $f(x) = \dfrac{3x - 2}{x^2 - 18}$.

Accepted Answer

All real numbers except $x = \sqrt{18}$ and $x = -\sqrt{18}$

Question 17

Find the domain and range of the function represented by the graph of $y = -x + 3$ for $x$ in $[0, 3]$.

Accepted Answer

Domain: $[0, 3]$, Range: $[0, 3]$

Question 18

Given the function $f(x) = x^2 - 2x - 3$, find the $x$-intercepts.

Accepted Answer

$x = -1, 3$

Question 19

A ball is thrown upward from the ground with an initial velocity of $32$ ft/s. Its height $h$ in feet after $t$ seconds is given by $h(t) = -16t^2 + 32t$. What is the maximum height reached by the ball?

Accepted Answer

$32$ ft

Precalculus Review: Distance, Circles, Functions, Lines, and Inequalities

Study Guide - Practice Questions

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