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 $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

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

Accepted Answer

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 $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

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 $$x^2 - 5x + 6$$ \u003c 0$$.

Accepted Answer

$$2 \u003c x \u003c 3$$

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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