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

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

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