Q: A motorboat travels upstream at a constant speed of 16 miles per hour. If it takes 20 minutes to reach a certain point, how far is the point from the starting location?

$$16 \times \frac{1}{3} = 5.33$$ miles

Question 1

A motorboat travels upstream at a constant speed of 16 miles per hour. If it takes 20 minutes to reach a certain point, how far is the point from the starting location?

Accepted Answer

$$16 	imes \frac{1}{3} = 5.33$$ miles

Question 2

Given the equation $$y = x^2$ + 4$$, which of the following best describes its graph?

Accepted Answer

A parabola opening upwards with vertex at $$(0, 4)$$

Question 3

A regulation doubles tennis court has an area of $$2808$$ square feet. If it is $$6$$ feet longer than twice its width, what is the width of the court?

Accepted Answer

$$36$$ feet

Question 4

Which of the following equations is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 5

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 6

Which of the following best describes the symmetry of the graph of $$y = x^2$?

Accepted Answer

Symmetric with respect to the $$y-$$axis

Question 7

Find the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$.

Accepted Answer

$$\frac{f(4) - f(1)}{4 - 1} = \frac{16 - 1}{3} = 5$$

Question 8

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

Accepted Answer

$$[2, \infty)$$

Question 9

Which of the following points lies on the graph of $$y = x^2$ - 2x$$?

Accepted Answer

$$(3, 3)$$

Question 10

Given $$f(x) = \frac{1}{x}$$ and $$g(x) = x^2$ + 2$$, find $$(f + g)(2).$$

Accepted Answer

$$(f + g)(2) = f(2) + g(2) = \frac{1}{2} + 6 = 6.5$$

Question 11

Which of the following describes the graph of $$y = |x|$$?

Accepted Answer

A V-shaped graph symmetric about the $$y-$$axis

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

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

Question 13

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input has exactly one output

Question 14

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

Accepted Answer

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

Question 15

Which of the following equations is symmetric with respect to the origin?

Accepted Answer

$$y = x^3$

Question 16

Find the difference quotient for $$f(x) = x^2$.

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h} = 2x + h$$

Question 17

Given $$f(x) = \sqrt{x}$$, for which values of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x \geq 0$$

Question 18

Which of the following best describes the graph of $$y = x^2$ - 4$$?

Accepted Answer

A parabola opening upwards with vertex at $$(0, -4)$$

Question 19

If $$f(x) = x^2$ and g(x) = 2x - 8$, find (f + g)(3$$)$$.

Accepted Answer

$$(f + g)(3) = f(3) + g(3) = 9 + (-2) = 7$$

College Algebra: Functions, Graphs, and Applications – Study Guide

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