$$\begin{bmatrix} 12 & 7 \\ 19 & 11 \end{bmatrix}$$

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

Question 1

Solve for $$x$$ over the complex numbers: $$2x^2 - 5x = -3$.

Accepted Answer

$$x = 1, x = 1.5$$

Question 2

Which of the following is the solution to $$\log_2$(x+2) + \log_2$(x-1) = 1$$?

Accepted Answer

$$x = 3$$

Question 3

Find the equation of the line perpendicular to $$y = 4x + 69$$ that passes through $$(7, 5).$$

Accepted Answer

$$y = -\frac{1}{4}x + \frac{33}{4}$$

Question 4

Solve the inequality and write the solution in interval notation: $$|2x - 3| \leq 11.$$

Accepted Answer

$$[-4, 7]$$

Question 5

Given the function $$f(x) = \frac{2x^2$ - 5x + 3}{x - 1}$$, find the $$y-$$intercept.

Accepted Answer

$$(0, 3)$$

Question 6

A population of bacteria starts at 1,000 and grows at a rate of 5% compounded quarterly. Which equation models the population after $$t$$ years?

Accepted Answer

$$P = 1000(1 + 0.05/4$$)^{4t}$$

Question 7

Find the determinant of the matrix $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}.$$

Accepted Answer

$$-10$$

Question 8

Expand the logarithmic expression: $$\log\left(\frac{x^2$y}{z^3$}\right).$$

Accepted Answer

$$2\log x + \log y - 3\log z$$

Question 9

Given the quadratic $$y = x^2$ + 2x + 3$$, what is the vertex of the parabola?

Accepted Answer

Question 10

Find the domain of the function $$f(x) = \frac{2x}{x^2$ - 9}.$$

Accepted Answer

$$x 
eq -3, x 
eq 3$$

Question 11

If $$\log_2$(x) + \log_2$(x-3) = 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 12

Which of the following is the equation of the circle with center $$(4, -6)$$ and radius $$8$$?

Accepted Answer

$$(x - 4)^2$ + (y + 6)^2$ = 64$$

Question 13

Find the sum $$\sum_{k=1}^{4} (k^2$ - 3).$$

Accepted Answer

$$24$$

Question 14

Given $$f(x) = x^2$ - 2x + 5$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 15

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

Accepted Answer

$$y = 3$$

Question 16

If $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 1 \ 5 & 3 \end{bmatrix}$$, what is $$AB$$?

Accepted Answer

$$\begin{bmatrix} 12 & 7 \ 19 & 11 \end{bmatrix}$$

Question 17

Find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = x^2$ - 4x.$$

Accepted Answer

$$2x + h - 4$$

Question 18

Given the function $$f(x) = \frac{x^2$ - 2x + 5}{x - 1}$$, find $$f(1).$$

Accepted Answer

Undefined

Question 19

Which of the following best describes the end behavior of $$f(x) = -2x^3$ + 5x^2$ - x + 7$$?

Accepted Answer

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

College Algebra Final Exam Review: Comprehensive Study Notes

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