Q: Which of the following is the correct system of equations for the augmented matrix $$\begin{bmatrix} 1 & 4 & 3 & | & 9 \\ 5 & 7 & 2 & | & 8 \\ 9 & 10 & 11 & | & 12 \end{bmatrix}$$?

$$\begin{cases} x + 4y + 3z = 9 \\ 5x + 7y + 2z = 8 \\ 9x + 10y + 11z = 12 \end{cases}$$

Q: If $$A = \begin{bmatrix} 5 & 10 \\ 15 & 20 \end{bmatrix}$$, what is $$4A$$?

$$\begin{bmatrix} 20 & 40 \\ 60 & 80 \end{bmatrix}$$

Question 1

Use substitution to determine whether $$x = 3 is a $$zero of the function $$f(x) = x^2$ + 5x + 7.$$

Accepted Answer

$$f(3) = 31$$, so $$x = 3 is $$not a zero.

Question 2

Which of the following is the correct vertical asymptote for the function $$f(x) = \dfrac{x^2$ - 5x + 4}{x + 2}$$?

Accepted Answer

$$x = -2$$

Question 3

What is the domain of the function $$f(x) = \dfrac{x^2$ - 5x + 4}{x + 2}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 4

Which of the following statements is TRUE about the vertical line test?

Accepted Answer

A graph is a function if any vertical line intersects the graph at most once.

Question 5

Which of the following functions is one-to-one?

Accepted Answer

$$y = 3^x$$

Question 6

Given $$f(x) = x^2$ - 5x + 4$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 4$$

Question 7

Which of the following is the correct $$y-$$intercept for $$f(x) = x^2$ - 5x + 4$$?

Accepted Answer

$$(0, 4)$$

Question 8

Which of the following is the correct change of base formula for $$\log_{6}{14}$$?

Accepted Answer

$$\dfrac{\ln{14}}{\ln{6}}$$

Question 9

Express $$\ln\left(\dfrac{x}{y}\right) as $$the sum or difference of logarithms.

Accepted Answer

$$\ln{x} - \ln{y}$$

Question 10

Simplify $$e^{\ln{(4x+1)}$$}$$.

Accepted Answer

$$4x + 1$$

Question 11

Solve for $$x$$: $$e^x = 13.$$

Accepted Answer

$$x = \ln{13}$$

Question 12

Which of the following is the correct system of equations for the augmented matrix $$\begin{bmatrix} 1 & 4 & 3 & | & 9 \ 5 & 7 & 2 & | & 8 \ 9 & 10 & 11 & | & 12 \end{bmatrix}$$?

Accepted Answer

$$\begin{cases} x + 4y + 3z = 9 \ 5x + 7y + 2z = 8 \ 9x + 10y + 11z = 12 \end{cases}$$

Question 13

If $$A = \begin{bmatrix} 5 & 10 \ 15 & 20 \end{bmatrix}$$, what is $$4A$$?

Accepted Answer

$$\begin{bmatrix} 20 & 40 \ 60 & 80 \end{bmatrix}$$

Question 14

Which of the following is the correct sum or difference expression for $$\log_5${7x}$$?

Accepted Answer

$$\log_5${7} + \log_5${x}$$

Question 15

Which of the following best describes the horizontal line test?

Accepted Answer

A function is one-to-one if and only if any horizontal line intersects the graph at most once.

Question 16

Which of the following is the correct expanded form for $$\log_3${x$$^{14}$$}$$?

Accepted Answer

$$14 \log_3${x}$$

Question 17

If $$f(x) = x^2$ - 3x - 4$$, use long division to determine if $$x + 1 is a $$factor.

Accepted Answer

No, because the remainder is not zero.

Question 18

Which of the following is the correct exponential form of $$\log_3${9} = 2$$?

Accepted Answer

$$3^2 = 9$

Question 19

Which of the following is the correct logarithmic form of $$e^x = 1$$?

Accepted Answer

$$x = \ln{1}$$

College Algebra Final Review: Comprehensive Study Notes

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