Q: Which of the following best describes the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 1$$?

$$f(x) \to -\infty as$$ $$x \to \pm\infty$$

Question 1

Solve for $$x$$: $$2x^2 - 5x - 3 = 0$.

Accepted Answer

$$x = -1, \; x = 3$$

Question 2

Which of the following is the correct equation of the line passing through the points $$(-3,4)$$ and $$(1,-7)$$?

Accepted Answer

$$y = -\frac{11}{4}x + \frac{1}{4}$$

Question 3

A population of a town increases according to the model $$P(t) = 2500e$$^{0.02t}$$, where t$ is time in years. Estimate the population in the year 2015 if t=12$ (years after 2003).

Accepted Answer

$$P(12) \approx 3170$$

Question 4

Suppose you invest \$$12,000 at an annual interest rate r$, compounded monthly. Which investment yields the greater return in 3 years: 7% compounded monthly or 7.2% compounded annually?

Accepted Answer

7% compounded monthly

Question 5

A hotel has 200 rooms. Rooms with kitchen facilities rent for \$$200 per night, and those without rent for \100 $$per night. On a night when the hotel was completely occupied, revenue was \$31,000. How many of each type of room does the hotel have?

Accepted Answer

55 with kitchen, 145 without

Question 6

Find the domain of the function $$f(x) = \frac{1}{x^2$ - 4}.$$

Accepted Answer

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

Question 7

Given $$f(x) = x^2$ - 2x + 1$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 8

Solve for $$x$$: $$\log_2$(x+2) + \log_2$(x-1) = 3.$$

Accepted Answer

$$x = 3$$

Question 9

Which of the following is the correct inverse of $$f(x) = \frac{2x+3}{5x-2}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{2x+3}{5x-2}$$

Question 10

Expand as much as possible: $$\log_2$\left(\frac{x^3$y^2$$}{$$z^5$$}\right)$.

Accepted Answer

$$3\log_2$ x + 2\log_2$ y - 5\log_2$ z$$

Question 11

Find the $$x-$$intercepts of $$f(x) = x^2$ - 2x - 3.$$

Accepted Answer

$$x = -1, \; x = 3$$

Question 12

Which of the following best describes the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 1$$?

Accepted Answer

$$f(x) 	o -\infty as$$ $$x 	o \pm\infty$$

Question 13

Divide and express the result in standard form: $$\frac{2x^2$ - 3x + 1}{x - 1}.$$

Accepted Answer

$$2x - 1 + \frac{-1}{x-1}$$

Question 14

For the function $$f(x) = x^3$ - 2x^2$ + x - 3$$, which of the following is a real root?

Accepted Answer

$$x = -1$$

Question 15

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

Accepted Answer

$$(3, -1)$$

Question 16

Find the domain of $$f(x) = \ln(x^2$ - 4).$$

Accepted Answer

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

Question 17

Which of the following is the correct solution for $$2^x = 8$$?

Accepted Answer

$$x = 3$$

Question 18

If $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 19

Which of the following is the correct solution to $$\log_3$(x) = 2$$?

Accepted Answer

$$x = 9$$

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