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

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

Question 1

Given the function $$f(x) = x^2$ - 4x + 9$$, what is the average rate of change of $$f(x) on $$the interval $$x = 1 to$$ $$x = 3$$?

Accepted Answer

$$0$$

Question 2

A company’s revenue function is $$R(x) = -\frac{1}{10}x^2$ + 100x$$, where $$x is $$the number of units sold. What is the maximum revenue, and at what value of $$x$$ does it occur?

Accepted Answer

Maximum revenue is $$2500 at$$ $$x = 500$$

Question 3

Which of the following describes the transformation of $$f(x) = x^2$ to g(x$$) = $$-(x+2)^2 - 3$?

Accepted Answer

Reflection over the $$x-$$axis, shift left 2, shift down 3

Question 4

Given the piecewise function $$M(x) = \begin{cases} -4 & x \leq 0 \ x+2 & x \u003e 0 \end{cases}$$, what is the domain of $$M(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 5

A closed box with a square base must have a volume of $$10\ 	ext{ft}^3. If $$the side of the base is $$x ft$$, what is the equation for the surface area $$S(x) of $$the box (with no top)?

Accepted Answer

$$S(x) = x^2$ + \frac{10}{x}$$

Question 6

For the polynomial $$p(x) = 3(x-1)^2$(x+3)(x+1)$$, which zero has even multiplicity and what does this mean for the graph at that zero?

Accepted Answer

$$x = 1$$, graph touches the $$x-$$axis

Question 7

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

Accepted Answer

$$[2, \infty)$$

Question 8

Which of the following rational functions has a vertical asymptote at $$x = 3$$ and a horizontal asymptote at $$y = 0$$?

Accepted Answer

$$r(x) = \frac{2x}{x-3}$$

Question 9

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 1$

Question 10

Solve the inequality $$5 - 3x \u003e 2(x - 4)$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2)$$

Question 11

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

Accepted Answer

$$(x + 2)^2$ - 4$$

Question 12

Which of the following is the inverse of $$f(x) = 3x - 1$$?

Accepted Answer

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

Question 13

For the rational function $$M(x) = \frac{x}{x^2$ - 9}$$, what is the domain?

Accepted Answer

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

Question 14

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

Accepted Answer

$$[0, \infty)$$

Question 15

Given the polynomial $$p(x) = x^4$ - 3x^2$ + 2$$, which of the following is a possible rational zero?

Accepted Answer

$$2$$

Question 16

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

Accepted Answer

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

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