Q: Which of the following is the correct result of multiplying the matrices $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \\ 1 & 3 \end{bmatrix}$$?

$$AB = \begin{bmatrix} 4 & 6 \\ 10 & 12 \end{bmatrix}$$

Q: A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

$$500 \times 2$$^{3}$$ = 4,000$$

Question 1

Which of the following statements best describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A hospital uses the function $$C(t) = 500e$$^{0.05t}$$ to model the cost of a medical procedure over time t$ (in years). What is the cost after 10 years?

Accepted Answer

$$C(10) = 500e$$^{0.5}$$ \approx 824.36$$

Question 3

Which of the following is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{2}$$

Question 4

A chemical reaction is modeled by the quadratic equation $$y = -2x^2$ + 8x + 5. $$What is the maximum value of $$y$$ and at what value of $$x$$ does it occur?

Accepted Answer

Maximum at $$x = 2$$, $$y = 13$$

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 6

If $$f(x) = \sqrt{x}$$ and $$g(x) = x + 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = \sqrt{2 + 1} = \sqrt{3}$$

Question 7

A company’s revenue is modeled by $$R(x) = 100x - 0.5x^2$, where x$ is the number of units sold. What is the maximum revenue and how many units should be sold to achieve it?

Accepted Answer

Maximum at $$x = 100$$, $$R(100) = 5,000$$

Question 8

Which of the following is the solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 9

Given the system of equations:

$$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 10

Which of the following is the correct result of multiplying the matrices $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \ 1 & 3 \end{bmatrix}$$?

Accepted Answer

$$AB = \begin{bmatrix} 4 & 6 \ 10 & 12 \end{bmatrix}$$

Question 11

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$500 	imes 2$$^{3}$$ = 4,000$$

Question 12

Which of the following is the correct logarithmic form of the equation $$10^3 = 1$$,000$$?

Accepted Answer

$$\log_{10}(1,000) = 3$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the sum of the functions $$f(x) = 2x$$ and $$g(x) = x^2$?

Accepted Answer

$$f(x) + g(x) = x^2$ + 2x$$

Question 15

A parabola opens upward and has its vertex at $$(3, -2). $$Which of the following is a possible equation for this parabola?

Accepted Answer

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

Question 16

Which of the following is the correct solution to the logarithmic equation $$\log_{2}(x) = 4$$?

Accepted Answer

$$x = 16$$

Question 17

A student invests $$1,000 in an $$account with an annual interest rate of $$6\%$$ compounded yearly. What will the balance be after 5 years? (Use $$A = P(1 + r)^t)$$

Accepted Answer

$$A = 1000(1.06)^5$ \approx 1,338.23$$

Question 18

Which of the following is the correct result of synthetic division of $$x^3$$ - $$6x^2 + 11x - 6$ by x - 1$?

Accepted Answer

$$x^2 - 5x + 6$

Question 19

Which of the following is the correct solution to the system using matrices:

$$\begin{cases} x + y = 4 \ 2x - y = 1 \end{cases}$$

Accepted Answer

$$(x, y) = (1.67, 2.33)$$

College Algebra Syllabus and Course Structure: Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard