Q: Which of the following describes the end behavior of the polynomial $f(x) = -2x^5 + 3x^2 - 1$?

As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to \infty$

Q: Which of the following is the correct graph for the rational function $f(x) = \dfrac{1}{x-2}$?

A graph with a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$

Question 1

Which of the following is the simplified form of $\left(2x^3y^{-2}\right)^2 \cdot \dfrac{y^3}{4x}$?

Question 2

A projectile is launched from the ground with an initial velocity such that its height after $t$ seconds is given by $h(t) = -16t^2 + 64t$. What is the maximum height reached by the projectile?

Accepted Answer

$128$ feet

Question 3

Solve the quadratic equation $2x^2 - 8x + 6 = 0$ using the quadratic formula.

Accepted Answer

$x = 1, x = 3$

Question 4

Which of the following is the conjugate of the complex number $3 - 4i$?

Accepted Answer

$3 + 4i$

Question 5

Solve the equation $\sqrt{2x + 3} = x - 1$ for $x$.

Accepted Answer

$x = 4$

Question 6

Which of the following is the solution set for $|2x - 5| < 7$?

Accepted Answer

$-1 < x < 6$

Question 7

Given the polynomial $f(x) = x^3 - 4x^2 + 4x$, which of the following is NOT a zero of $f(x)$?

Accepted Answer

$4$

Question 8

Divide $2x^3 - 3x^2 + 4x - 5$ by $x - 2$ using synthetic division. What is the remainder?

Accepted Answer

$1$

Question 9

Which of the following describes the end behavior of the polynomial $f(x) = -2x^5 + 3x^2 - 1$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o \infty$

Question 10

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

Accepted Answer

$x 
eq 3, x 
eq -3$

Question 11

Solve the quadratic inequality $x^2 - 5x + 6 < 0$.

Accepted Answer

$2 < x < 3$

Question 12

Which of the following is the correct graph for the rational function $f(x) = \dfrac{1}{x-2}$?

Accepted Answer

A graph with a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$

Question 13

If $f(x) = x^2 - 6x + 8$, what is the vertex of the parabola?

Accepted Answer

$(3, -1)$

Question 14

Solve the rational equation $\dfrac{2}{x} + 1 = \dfrac{5}{x}$.

Accepted Answer

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

Question 15

Which of the following is the simplified form of $\dfrac{3 + 2i}{1 - i}$?

Accepted Answer

$\dfrac{1 + 5i}{2}$

Question 16

A rectangular garden is to be built using 40 meters of fencing. If the length is twice the width, what are the dimensions that maximize the area?

Accepted Answer

Length $= 10$ m, Width $= 5$ m

Question 17

Which of the following is the solution to the equation $x^4 - 5x^2 + 4 = 0$?

Accepted Answer

$x = 1, -1, 2, -2$

Question 18

Find all real solutions to $|x + 3| = 7$.

Accepted Answer

$x = 4, x = -10$

Question 19

Which of the following describes the multiplicity of the zero $x = 2$ for the polynomial $f(x) = (x - 2)^3(x + 1)$?

Accepted Answer

Multiplicity 3

Question 20

Which of the following is the horizontal asymptote of the rational function $f(x) = \dfrac{3x^2 + 2}{x^2 - 5}$?

Accepted Answer

$y = 3$

College Algebra: Quadratic and Polynomial Functions, Equations, and Inequalities Study Guide

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