Question 1

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 2

What is the result of $$(5 - 2i) + (3 + 3i)$$?

Accepted Answer

$$8 + i$$

Question 3

If $$i^2 = -1$, what is the value of (2$$ + $$3i)^2$$?

Accepted Answer

$$-5 + 12i$$

Question 4

Which of the following describes the end behavior of $$f(x) = -4x^3$(x-1)^2(x+5$$)$?

Accepted Answer

Rises left, falls right

Question 5

Given $$f(x) = x^2$ - 4x + 6$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 2)$$

Question 6

A football is kicked and its height is modeled by $$f(x) = -0.01x^2$ + 1.18x + 2. $$What is the maximum height of the punt?

Accepted Answer

$$f(59) = 36.81$$ feet

Question 7

Which of the following is NOT a polynomial function?

Accepted Answer

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

Question 8

What is the domain of $$f(x) = \frac{x^2$ - 25}{x - 5}$$?

Accepted Answer

$$x 
eq 5$$

Question 9

Which of the following is the correct horizontal asymptote for $$f(x) = \frac{9x^2$}{3x^2$ + 1}$$?

Accepted Answer

$$y = 3$$

Question 10

Using the Rational Zero Theorem, which of the following is a possible rational zero of $$f(x) = 4x^5$ + 12x^4$ - x - 3$$?

Accepted Answer

$$\frac{3}{4}$$

Question 11

Solve the quadratic equation $$x^2 + 2x + 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = -1 \pm 2i$$

Question 12

Which statement about the zeros of $$f(x) = (x-2)^2$(x+3) is $$correct?

Accepted Answer

The graph touches the x-axis at $$x=2$$ and crosses at $$x=-3$$

Question 13

Given $$f(x) = \frac{3x-3}{x-2}$$, what is the vertical asymptote?

Accepted Answer

$$x = 2$$

Question 14

Which of the following describes the graph of $$f(x) = x^4$ - 4x^2$ as x$$ 	o \infty$$?

Accepted Answer

Rises to infinity

Question 15

If $$f(x) = x^3$ + 2x^2$ - 4x - 8$$, which of the following is a zero of $$f(x)$$?

Accepted Answer

$$x = -4$$

Question 16

Which of the following is a property of the roots of a polynomial equation with real coefficients?

Accepted Answer

If $$a + bi is a $$root, then $$a - bi is $$also a root.

Question 17

What is the solution set for the inequality $$x^2 - x$$ \u003e 20$$?

Accepted Answer

$$x  5$$

Question 18

Which of the following is the correct application of Descartes’ Rule of Signs for $$f(x) = x^3$ + 2x^2$ + 5x + 4$$?

Accepted Answer

There are no positive real zeros.

Question 19

Given $$f(x) = \frac{x}{x^2$ + 25}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers

Question 20

Which of the following is the correct factorization for a fourth-degree polynomial with zeros at $$-2, 2, i$$, and $$-i$$?

Accepted Answer

$$f(x) = a(x + 2)(x - 2)(x - i)(x + i)$$

Polynomial and Rational Functions: Key Concepts and Graphs

Study Guide - Practice Questions