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

As $$x \to \pm\infty$$, $$f(x) \to \infty$$

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 $$f(x) = \dfrac{2}{x^2$ - 9}$$?

Accepted Answer

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

Question 4

Given $$f(x) = x^2$ + x - 2$$ and $$g(x) = 3x + 5$$, find $$(f + g)(0).$$

Accepted Answer

$$3$$

Question 5

For the rational function $$f(x) = \dfrac{x^2$ - x - 2}{2x^2$ + x - 1}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = -1$$

Question 6

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

Accepted Answer

$$5$$

Question 7

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

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o \infty$$

Question 8

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

Accepted Answer

$$x = 0$$

Question 9

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

Accepted Answer

$$x = 5.861$$

Question 10

Charley puts $$2500 in a savings account that compounds interest quarterly at a rate of 4.75$$\%$$. How much money will he have in his account after 7$ years? (Use A = P$$\left(1 + \frac{r}{n}\$$right)^{nt}$ and round to the nearest cent.)

Accepted Answer

$$3492.13$$

Question 11

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

Accepted Answer

$$x = \log_5$ 27$$

Question 12

Solve the system of equations: $$3x - 2y = 14$$ and $$5x + y = 23.$$

Accepted Answer

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

Question 13

What is the horizontal asymptote of the function $$f(x) = \dfrac{x^2$ - 4x + 2}{x - 1}$$?

Accepted Answer

$$y = x$$

Question 14

Given $$f(x) = x^2$ - 2x + 4$$, use the difference quotient $$\dfrac{f(x + h) - f(x)}{h} to $$find the simplified expression.

Accepted Answer

$$2x + h - 2$$

Question 15

Which of the following intervals describes where the function below is increasing? (Refer to the graph in question 11.)

Accepted Answer

$$(a, b)$$ where the graph rises left to right

Question 16

If $$\log_6$ (2x + 3) - \log_6$ (x + 4) = 1$$, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the correct domain for $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$[4, \infty)$$

Question 18

Given $$f(x) = \sqrt{x - 2}$$ and $$g(x) = x^2$ - 1$$, find $$g(f(x))$$ and its domain.

Accepted Answer

$$g(f(x)) = x - 3$$,\ x \geq 2$

Question 19

Which of the following is the correct range for the quadratic function $$f(x) = -x^2$ + 4x - 3$$?

Accepted Answer

$$(-\infty, 1]$$

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