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

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

Question 1

Solve the linear equation: $$-2(3x + 4) - 2x = 5(x - 2) - 4$$

Accepted Answer

$$x = -4$$

Question 2

Which of the following is the domain of the function $$f(x) = \dfrac{x-1}{x^2$-3}$$?

Accepted Answer

$$(-\infty, -\sqrt{3}) \cup (-\sqrt{3}, \sqrt{3}) \cup (\sqrt{3}, \infty)$$

Question 3

A manufacturer has a monthly fixed cost of $$150,000$$ and a production cost of $$18$$ for each unit produced. The product sells for $$24$$ per unit. Let $$x$$ represent the number of units sold. Which function represents the total cost?

Accepted Answer

$$C(x) = 150,000 + 18x$$

Question 4

Solve the quadratic equation: $$x^2 - 10x = 3$

Accepted Answer

$$x = 5 \pm \sqrt{28}$$

Question 5

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

Accepted Answer

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

Question 6

A farmer has $$1000 ft of $$fence to enclose a rectangular area. If there is a barn on one side, so no fencing is required there, what is the maximum area that can be enclosed?

Accepted Answer

$$250,000 sq ft$$

Question 7

Solve the inequality: $$2(2x - 1) \u003e 4(x + 2) - 4x$$

Accepted Answer

$$x \u003e 2$$

Question 8

Which of the following is the inverse of the function $$f(x) = 4x - 8$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 8}{4}$$

Question 9

Given $$f(x) = x^2$ - 4x + 1$$ and $$g(x) = 2x^2$ + 5x + 1$$, find $$(f + g)(2).$$

Accepted Answer

$$15$$

Question 10

Solve for $$x$$: $$\sqrt{2x + 3} = 7$$

Accepted Answer

$$x = 23$$

Question 11

Which of the following is the correct solution to $$0.8^x = 4$$? (Round to the nearest hundredth)

Accepted Answer

$$x = -7.22$$

Question 12

If $$25,000 is $$invested at an annual interest rate of $$2.5\%$$ compounded quarterly, how much will be in the account after $$25$$ years? (Round to the nearest cent)

Accepted Answer

$$A = 43,000.77$$

Question 13

Which of the following is the correct equation for the vertical asymptote of $$f(x) = \dfrac{x-1}{x^2$-3}$$?

Accepted Answer

$$x = \pm \sqrt{3}$$

Question 14

Which function best models data that increases rapidly and then levels off, as seen in population growth with limited resources?

Accepted Answer

Logarithmic

Question 15

Solve for $$x$$: $$\log_2$(x) + \log_2$(x) = 2$$

Accepted Answer

$$x = 4$$

Question 16

Which of the following is the correct exponential form of $$\sqrt[3]{x^7$}$$?

Accepted Answer

$$x^{7/3}$$

Question 17

Given the system: $$\begin{cases} -3x + 2y = 11 \ x - y = -3 \end{cases}$$, what is the solution?

Accepted Answer

$$(-1, -4)$$

Question 18

Which of the following is the correct result of $$(3 - 5i)(2 - 4i) in $$standard form $$a + bi$$?

Accepted Answer

$$-14 + 22i$$

Question 19

If $$f(x) = (x-2)^2$ - 7$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -7)$$

Question 20

Which of the following best describes the range of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$[0, \infty)$$

College Algebra Final Exam Review: Comprehensive Study Notes

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