Question 1

Which of the following is NOT a polynomial function?

Accepted Answer

$$h(x) = -3\sqrt{x} + \sqrt{2}x^2$ + 5$$

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use the Remainder Theorem to find the remainder when $$f(x) is $$divided by $$x - 2.$$

Accepted Answer

$$f(2) = -2$$

Question 3

Which of the following statements is TRUE according to the Factor Theorem?

Accepted Answer

If $$x - c is a $$factor of $$f(x)$$, then $$f(c) = 0.$$

Question 4

What is the domain of the rational function $$f(x) = \frac{x^2$ - 9}{x - 3}$$?

Accepted Answer

$$x 
eq 3$$

Question 5

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

Accepted Answer

Rises to the left, falls to the right

Question 6

Find all possible rational zeros of $$f(x) = 2x^3$ - 3x^2$ + x - 6$$ using the Rational Zero Theorem.

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6, \pm\frac{1}{2}, \pm\frac{3}{2}$$

Question 7

What is the vertex of the parabola $$f(x) = 2x^2$ - 8x + 3$$?

Accepted Answer

$$(2, -5)$$

Question 8

A company’s daily profit is modeled by $$P(x) = -3x^2$ + 36x - 150$$, where $$x is $$the number of cakes produced. How many cakes should be produced to maximize profit?

Accepted Answer

$$x = 12$$

Question 9

Which of the following is the correct solution to the quadratic equation $$2x^2 - 4x - 6 = 0$ using the quadratic formula?

Accepted Answer

$$x = 3, x = -1$$

Question 10

Which of the following is the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 11

Given $$f(x) = \frac{2x}{x^2$ + 4}$$, which of the following is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 12

If a polynomial $$f(x)$$ has a zero at $$x = 2$$ with multiplicity 3, what happens to the graph at $$x = 2$$?

Accepted Answer

The graph crosses the x-axis at $$x = 2$$

Question 13

Which of the following rational functions has a domain of all real numbers except $$x = -3$$?

Accepted Answer

$$k(x) = \frac{1}{x + 3}$$

Question 14

Which of the following best describes the graph of $$f(x) = \frac{1}{x}$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0$$

Question 15

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the end behavior of the graph?

Accepted Answer

Rises to the left, rises to the right

Question 16

Which of the following is the correct process for synthetic division of $$2x^3$$ - $$3x^2 + 4$ by x - 1$?

Accepted Answer

Use 1 as $$c$$ and write coefficients $$[2, -3, 0, 4]$$

Question 17

A ball is thrown upward with height $$h(t) = -16t^2$ + 32t + 15. $$What is the maximum height of the ball?

Accepted Answer

$$h(2) = 47$$

Question 18

Which of the following is a rational function?

Accepted Answer

$$g(x) = \frac{x^2$ + 1}{x - 2}$$

Key Concepts in Polynomial and Rational Functions for College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards