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

$$y \to \infty as$$ $$x \to \infty$$ and $$y \to \infty as$$ $$x \to -\infty$$

Question 1

Find the slope of the line passing through the points $$(-7, -2)$$ and $$(4, 3). $$Which of the following is correct?

Accepted Answer

$$\displaystyle \frac{5}{11}$$

Question 2

Which of the following is the equation of the line containing the point $$(5, -1)$$ and perpendicular to the line $$y = 2x + 1$$?

Accepted Answer

$$y + 1 = -\frac{1}{2}(x - 5)$$

Question 3

What is the domain of the function $$f(x) = \frac{2}{x^2$ - 9}$$?

Accepted Answer

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

Question 4

Given $$f(x) = x^2$ + x - 2$$ and $$g(x) = 3x + 5$$, what is $$f(g(0))$$?

Accepted Answer

$$18$$

Question 5

Which of the following describes the horizontal asymptote (H.A.) of $$f(x) = \frac{x^2$ - x - 2}{2x^2$ + x - 1}$$?

Accepted Answer

$$y = \frac{1}{2}$$

Question 6

Given the piecewise function $$f(x) = \begin{cases} -2x - 1, & x \leq -3 \ 1, & -3 \u003c x \u003c 2 \ x^2$, & x \geq 2 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$5$$

Question 7

Which of the following intervals describes where the function in the graph is increasing?

Accepted Answer

$$(-\infty, -2) \cup (1, 3)$$

Question 8

If $$f(x) = x^2$ - 2x + 1$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h - 2$$

Question 9

Given $$f(x) = x^4$ + 4x^3$ + x^2$ - 6$$, and $$1 is a $$zero, which of the following is a possible other zero?

Accepted Answer

$$-3$$

Question 10

Which of the following is the correct logarithmic form of the equation $$5^x = 27$$?

Accepted Answer

$$x = \log_5$ 27$$

Question 11

Solve for $$x$$: $$3^x = 411. $$Round your answer to three decimal places.

Accepted Answer

$$x = \log_3$ 411$$

Question 12

Which of the following is the solution to the system: $$3x - 2y = 8$$, $$5x + y = 23$$?

Accepted Answer

$$x = 3,\ y = 4$$

Question 13

If Charley puts $$2500 in a savings account that compounds interest quarterly at 4.75\% annual rate, how much money will he have after 7 years? Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$.

Accepted Answer

$$A = 2500 \left(1 + \frac{0.0475}{4}\$$right)^{28}$$

Question 14

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

Accepted Answer

$$y 	o \infty as$$ $$x 	o \infty$$ and $$y 	o \infty as$$ $$x 	o -\infty$$

Question 15

Given $$f(x) = \sqrt{x-2}$$ and $$g(x) = x^2$ - 1$$, what is the domain of $$g(f(x))$$?

Accepted Answer

$$x \geq 2$$

Question 16

Which of the following is the correct solution for $$\log_6$ (2x + 3) - \log_6$ (x + 2) = \log_6$ (x - 2)$$?

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the correct equation for the vertical asymptote (V.A.) of $$f(x) = \frac{x^2$ + 4x + 2}{x - 1}$$?

Accepted Answer

$$x = 1$$

Question 18

Which of the following is the correct transformation for $$f(x) = \left| \frac{1}{2}x \right| - 3$$?

Accepted Answer

Vertical shift down 3 units and horizontal stretch by factor of 2

Question 19

Given $$f(x) = x^2$ + x - 2$$ and $$g(x) = 3x + 5$$, what is $$\frac{f(x)}{g(x)}$$ when $$x = 0$$?

Accepted Answer

$$-0.4$$

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