Q: Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

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

Q: A loan of $$\10$$,000$ is taken out at an annual interest rate of 6%, compounded monthly. What is the value of the loan after 3 years?

$$10,000 \times (1 + \frac{0.06}{12}$$)^{36}$$

Question 1

Which of the following best describes the inverse of a function $$f(x)$$?

Accepted Answer

A function that undoes the action of $$f(x)$$, such that $$f(f^{-1}(x)) = x$.

Question 2

Given $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 3$

Question 3

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 4

Which of the following is the correct solution set for the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 5

A car’s value depreciates exponentially at a rate of 12% per year. If the car is worth $$\20$$,000$ now, what will its value be in 5 years?

Accepted Answer

$$20,000 	imes (0.88)^5$

Question 6

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 7

If $$f(x) = \dfrac{1}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 8

Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

Accepted Answer

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

Question 9

A loan of $$\10$$,000$ is taken out at an annual interest rate of 6%, compounded monthly. What is the value of the loan after 3 years?

Accepted Answer

$$10,000 	imes (1 + \frac{0.06}{12}$$)^{36}$$

Question 10

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 11

Which of the following is the correct expression for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 13

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 14

A system of equations is inconsistent if:

Accepted Answer

It has no solution.

Question 15

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 16

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

Accepted Answer

$$(2)(4) - (1)(3) = 8 - 3 = 5$$

Question 17

Which of the following is the correct solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 18

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$R(3) = 23 at$$ $$x = 3$$ thousand units.

Question 19

Which of the following is the correct solution to the system: $$\begin{cases} x + y + z = 6 \ 2x - y + z = 3 \ x + 2y - z = 4 \end{cases}$$?

Accepted Answer

$$x = 1, y = 2, z = 3$$

College Algebra Course Syllabus and Weekly Study Guide

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