Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function of the form $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where all coefficients $$a_i$$ are real numbers and $$n$ is a non-negative integer.

Question 2

Given the polynomial $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 3

Which of the following best describes the graph of $$y = \frac{1}{x-2}$$?

Accepted Answer

It has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0.$$

Question 4

Solve the inequality $$|2x - 5| \u003c 7.$$

Accepted Answer

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

Question 5

Which of the following is the correct partial fraction decomposition of $$\frac{5x+3}{(x+1)(x-2)}$$?

Accepted Answer

$$\frac{2}{x+1} + \frac{3}{x-2}$$

Question 6

Which of the following equations represents a circle centered at $$(2, -3)$$ with radius $$5$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 25$

Question 7

If $$f(x) = 2^x$$ and $$g(x) = \log_2$ x$$, which statement is true?

Accepted Answer

$$f$$ and $$g$$ are inverse functions of each other.

Question 8

Solve for $$x$$: $$3^{2x} = 81$.

Accepted Answer

$$x = 2$$

Question 9

Which of the following is the sum of the first $$10$$ terms of the arithmetic sequence where $$a_1 = 3$ and d = 2$?

Accepted Answer

$$85$$

Question 10

A population of bacteria triples every 4 hours. If the initial population is $$200$$, what is the population after $$12$$ hours?

Accepted Answer

$$5400$$

Question 11

Which of the following is the correct solution to the system of equations using Cramer's Rule?

$$\begin{cases} 2x + 3y = 8 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2$$, $$y = 1$$

Question 12

Which of the following is the equation of a parabola that opens upward with vertex at $$(1, -2)$$?

Accepted Answer

$$y = (x-1)^2$ - 2$$

Question 13

Which of the following is the correct binomial expansion for $$(x+2)^3$$?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 14

Which of the following is the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$?

Accepted Answer

$$6$$

Question 15

Given the matrix $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$, what is $$\det(A)$$?

Accepted Answer

$$-2$$

Question 16

Which of the following best describes the graph of $$y = \log_{10} x$$?

Accepted Answer

It passes through $$(1, 0)$$ and has a vertical asymptote at $$x = 0.$$

Question 17

Which of the following is the correct solution to the rational inequality $$\frac{x-3}{x+2} \u003e 0$$?

Accepted Answer

$$x \u003e 3 or$$ $$x \u003c -2$$

Question 18

Which of the following is the correct equation for a hyperbola centered at the origin with vertices at $$(\pm 4, 0)$$ and asymptotes $$y = \pm x$$?

Accepted Answer

$$\frac{x^2$}{16} - \frac{y^2$}{16} = 1$$

MAC1140 Precalculus Algebra Syllabus and Course Overview

Guida di studio - Domande di pratica

Study guide - Flashcard