Q: Given the function $$m(x) = x^3$ - 2x$$, which of the following describes its end behavior?

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

Q: Given $$f(x) = 2x^2$ + 8x - 8$$ and $$g(x) = 2 - 4x$$, find $$(f \circ g)(x)$$ and state its domain.

$$(f \circ g)(x) = 2(2-4x)^2$ + 8(2-4x) - 8$$, \text{ domain: } \mathbb{R}$

Q: Given $$p(x) = x + 3$$ and $$q(x) = x - 2$$, are $$p$$ and $$q$$ inverses of each other?

No, because $$(p \circ q)(x) \neq x$$

Question 1

Given the function $$f(x) = -2(x-3)^2$ + 4$$, what is the vertex of the graph of $$f$$?

Accepted Answer

$$(3, 4)$$

Question 2

A rectangular garden is enclosed by 400 ft of fencing. Let $$w$$ represent the width and $$l$$ the length. Which quadratic function expresses the area $$A in $$terms of $$w$$?

Accepted Answer

$$A(w) = w(200 - w)$$

Question 3

Given the function $$m(x) = x^3$ - 2x$$, which of the following describes its end behavior?

Accepted Answer

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

Question 4

Which of the following is the equation for a function whose graph is the result of reflecting $$y = x$$ about the x-axis, then shifting it 4 units to the right and 2 units down?

Accepted Answer

$$y = -(x-4) - 2$$

Question 5

Given $$f(x) = \frac{9}{x-3}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 6

Given $$f(x) = \frac{9}{x-3}$$, what is the y-intercept of the graph?

Accepted Answer

$$(0, -3)$$

Question 7

Given $$P(x) = -8x^2$ + 5000x - 8000$$, where $$P is $$the daily profit and $$x is $$the number of units produced, how many units should be produced each day to yield a maximum profit?

Accepted Answer

$$x = 312.5$$

Question 8

Which of the following is the correct method to find the maximum profit for $$P(x) = -8x^2$ + 5000x - 8000$$?

Accepted Answer

Find the vertex using $$x = -\frac{b}{2a}$$

Question 9

Given $$m(x) = x^3$ - 2x$$, determine algebraically whether $$m is $$even, odd, or neither.

Accepted Answer

Odd

Question 10

Given $$f(x) = 2x^2$ + 8x - 8$$ and $$g(x) = 2 - 4x$$, find $$(f \circ g)(x)$$ and state its domain.

Accepted Answer

$$(f \circ g)(x) = 2(2-4x)^2$ + 8(2-4x) - 8$$, 	ext{ domain: } \mathbb{R}$

Question 11

Evaluate $$\ln 9 - 2 \ln 4 + \log_e 1.$$

Accepted Answer

$$2 \ln 3 - 2 \ln 2$$

Question 12

Given $$y = \frac{2x^2$ - 12}{x^2$ - 9}$$, what are the equations of all asymptotes?

Accepted Answer

Vertical: $$x = 3, x = -3$$; Horizontal: $$y = 2$$

Question 13

Given $$p(x) = x + 3$$ and $$q(x) = x - 2$$, are $$p$$ and $$q$$ inverses of each other?

Accepted Answer

No, because $$(p \circ q)(x) 
eq x$$

Question 14

Which of the following best describes the domain and range of the function $$h(x) = \sqrt{x-3}$$?

Accepted Answer

Domain: $$[3, \infty)$$; Range: $$[0, \infty)$$

Question 15

If a function $$f$$ decreases on $$(-\infty, 4)$$ and increases on $$(4, \infty)$$, what can be said about $$x = 4$$?

Accepted Answer

$$x = 4 is a $$local minimum

Question 16

Which of the following is the correct composition for $$f(x) = 3x + 2$$ and $$g(x) = x - 3$$?

Accepted Answer

$$(f \circ g)(x) = 3(x-3) + 2$$

Question 17

Which transformation sequence produces the graph of $$y = -\sqrt{x-4} - 2$$ from $$y = \sqrt{x}$$?

Accepted Answer

Shift right 4 units, reflect over x-axis, shift down 2 units

Question 18

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

Accepted Answer

$$4$$

Question 19

Given $$f(x) = \frac{9}{x-3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

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