Domain: $x \neq -4$, Range: $(-3, \infty)$, Vertical asymptote: $x = -4$, Horizontal asymptote: $y = -3$, Intercept: $(0, -\frac{11}{16})$

$g^{-1}(x) = \frac{5x+2}{x-1}$, Domain: $x \neq 1$

Question 1

Which of the following is the correct factorization of $x^2 - 9x$?

Accepted Answer

$x(x-9)$

Question 2

Given the quadratic equation $x^2 + 8x = 20$, which method would NOT be appropriate for solving it?

Accepted Answer

Graphing only

Question 3

Find the center and radius of the circle: $(x-3)^2 + y^2 = 64$.

Accepted Answer

Center: $(3,0)$, Radius: $8$

Question 4

What is the equation of the circle with center $(1,-5)$ that passes through the point $(3,4)$?

Accepted Answer

$(x-1)^2 + (y+5)^2 = 85$

Question 5

A ball is thrown upwards. Its height in feet is given by $h(t) = -16t^2 + 80t + 30$. How long does it take for the ball to reach its maximum height?

Accepted Answer

$t = 2.5$ seconds

Question 6

Find the domain and range of the function $f(x) = x^2 - 6x - 12$.

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[-16, \infty)$

Question 7

Which of the following is the correct difference quotient for $f(x) = \frac{2}{x}$?

Accepted Answer

$\frac{\frac{2}{x+h} - \frac{2}{x}}{h}$

Question 8

Solve the rational equation: $\frac{3}{x-4} = \frac{2}{x+4}$.

Accepted Answer

$x = -5$

Question 9

Find the domain, range, asymptotes, and intercepts of the function $y = \frac{1}{(x+4)^2} - 3$.

Accepted Answer

Domain: $x 
eq -4$, Range: $(-3, \infty)$, Vertical asymptote: $x = -4$, Horizontal asymptote: $y = -3$, Intercept: $(0, -\frac{11}{16})$

Question 10

Does the function $y = x^2 + 7x - 2$ have an inverse? Why?

Accepted Answer

No, because it is not one-to-one over $(-\infty, \infty)$.

Question 11

Find the inverse of the function $f(x) = (x-2)^3 + 7$.

Accepted Answer

$f^{-1}(x) = \sqrt[3]{x-7} + 2$

Question 12

Find the domain, range, and equation of the asymptote for $y = 2^{x+1} + 5$.

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $(5, \infty)$, Asymptote: $y = 5$

Question 13

Find the $x$-intercept and $y$-intercept of the function $f(x) = 5^{x+1} - 1$.

Accepted Answer

$x$-intercept: $-2.0$, $y$-intercept: $(0, 24)$

Question 14

Find the equation of the exponential function $y = a^x$ that passes through the point $(-3, 1)$.

Accepted Answer

$y = 2^x$

Question 15

Solve the equation $5^{2x-1} = \sqrt{5}$ by relating the bases.

Accepted Answer

$x = \frac{1}{2}$

Question 16

Evaluate the function $f(x) = 5^x$ at $x = -1, 0, \frac{1}{2}, 1, 2$. Which is the correct set of values?

Accepted Answer

$f(-1) = \frac{1}{5}, f(0) = 1, f(\frac{1}{2}) = \sqrt{5}, f(1) = 5, f(2) = 25$

Question 17

Which of the following describes the vertical asymptote of $f(x) = \frac{2x+1}{x-3}$?

Accepted Answer

$x = 3$

Question 18

Find the inverse of $g(x) = \frac{x+2}{x-5}$ and state the domain of $g^{-1}(x)$.

Accepted Answer

$g^{-1}(x) = \frac{5x+2}{x-1}$, Domain: $x 
eq 1$

Precalculus Exam Review: Factoring, Quadratics, Circles, Rational and Exponential Functions

Study Guide - Practice Questions