Question 1

Given the function $$f(x)$$ shown in the graph, determine the intervals on which $$f(x) is $$increasing.

Accepted Answer

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

Question 2

A farmer has 200 ft of fencing to enclose a rectangular area. If the enclosed area is $$x$$ feet long, express the area $$A as a $$function of $$x.$$

Accepted Answer

$$A(x) = x(200 - 2x)$$

Question 3

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

Accepted Answer

The graph where the lines intersect at $$(3, -1)$$

Question 4

For the function $$f(x) = x^2$ - 3x + 2$$, construct and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h - 3$$

Question 5

Find all $$x-$$intercepts of the function $$f(x) = x^2$ - 4x + 3.$$

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 6

Suppose $$f(x) is an $$even function. Which of the following statements is true?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain of $$f$$

Question 7

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

Accepted Answer

$$[1, \infty)$$

Question 8

Which of the following is the correct equation for a parabola that opens downward and has vertex at $$(2, 3)$$?

Accepted Answer

$$y = -a(x-2)^2$ + 3$$

Question 9

If $$f(x) = 2x^3$ - x^2$ + 5$$, what is $$f(-x)$$?

Accepted Answer

$$-2x^3$$ - $$x^2 + 5$

Question 10

A sound wave travels at 340 m/s. If its frequency is 850 Hz, what is its wavelength?

Accepted Answer

$$0.4 m$$

Question 11

Which transformation maps the graph of $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units, up 2 units

Question 12

If $$f(x) = \frac{1}{x}$$, which of the following describes the end behavior as $$x 	o 0^+$$?

Accepted Answer

$$f(x) 	o +\infty$$

Question 13

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$2x + h$$

Question 14

Given the function $$f(x) = \sin(x)$$, which of the following statements is true?

Accepted Answer

$$f(x) is an $$odd function

Question 15

Which of the following is the correct interval notation for the solution set of $$x^2$$ \u003c 9$$?

Accepted Answer

$$(-3, 3)$$

Question 16

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

Accepted Answer

$$(f \circ g)(x) = (x+1)^2$

Question 17

Which of the following is the correct graph for $$y = -|x| + 2$$?

Accepted Answer

A 'V' shape opening downward with vertex at $$(0, 2)$$

Question 18

If $$f(x) = x^3$ - 2x^2$ + x$$, what is the slope of the tangent line at $$x = 1$$?

Accepted Answer

$$0$$

Question 19

Suppose $$h(x) is a $$function such that $$h(x) = h(-x)$$ for all $$x. $$Which of the following must be true?

Accepted Answer

$$h(x) is $$even$

College Algebra: Functions, Graphs, and Applications Study Guide

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