Q: For the function $f(x) = x^2 - 2x - 2$, what are the x-intercepts?

$x = 1 + \\sqrt{3}, \\ 1 - \\sqrt{3}$

Q: Which of the following best describes a vertical asymptote?

A vertical line $x = a$ where $f(x)$ approaches $\\infty$ or $-\\infty$ as $x$ approaches $a$.

Q: What is the domain of the function $g(x) = \\frac{2x^2 - 7x + 4}{x - 4}$?

$(-\\infty, 4) \\cup (4, \\infty)$

Q: If a function $f(x)$ has a horizontal asymptote at $y = 5$, what does this mean?

As $x$ approaches $\\infty$ or $-\\infty$, $f(x)$ approaches $5$.

Q: If the graph of $y = f(x)$ has a vertical asymptote at $x = -4$, what is the domain of $f(x)$?

$(-\\infty, -4) \\cup (-4, \\infty)$

Question 1

Given the function $f(x) = -3x(x^2 - 16)$, which of the following lists all real solutions to $f(x) = 0$?

Accepted Answer

$x = -4, 0, 4$

Question 2

What is the y-intercept of the function $f(x) = -3x + 2$?

Accepted Answer

$y = 2$

Question 3

For the function $f(x) = x^2 - 2x - 2$, what are the x-intercepts?

Accepted Answer

$x = 1 + \sqrt{3}, \ 1 - \sqrt{3}$

Question 4

Given the graph of $y = f(x)$ with domain $[-2, 4]$ and range $[0, 6]$, which statement is true?

Accepted Answer

The smallest value of $f(x)$ is $0$ and the largest is $6$.

Question 5

Which of the following best describes a vertical asymptote?

Accepted Answer

A vertical line $x = a$ where $f(x)$ approaches $\infty$ or $-\infty$ as $x$ approaches $a$.

Question 6

What is the domain of the function $g(x) = \frac{2x^2 - 7x + 4}{x - 4}$?

Accepted Answer

$(-\infty, 4) \cup (4, \infty)$

Question 7

Which interval describes where the function $y = f(x)$ is increasing, given the graph with increasing intervals $(-\infty, 0)$ and $(2, 3)$?

Accepted Answer

$(-\infty, 0) \cup (2, 3)$

Question 8

If a function $f(x)$ has a horizontal asymptote at $y = 5$, what does this mean?

Accepted Answer

As $x$ approaches $\infty$ or $-\infty$, $f(x)$ approaches $5$.

Question 9

Given $f(x)$ is constant on the interval $(3, 5)$, which statement is true?

Accepted Answer

For any $x_1, x_2$ in $(3, 5)$, $f(x_1) = f(x_2)$.

Question 10

A function $f(x)$ changes from increasing to decreasing at $x = 2$. What does $f(x)$ have at $x = 2$?

Accepted Answer

A relative maximum

Question 11

Given the function $f(x) = x^2 - 2x - 2$, what is the y-intercept?

Accepted Answer

$y = -2$

Question 12

Which of the following is the correct definition of a relative minimum?

Accepted Answer

A point $(c, f(c))$ where $f(x)$ changes from decreasing to increasing.

Question 13

For the function $g(x) = \frac{2x^2 - 7x + 4}{x - 4}$, what is the y-intercept?

Accepted Answer

$y = -1$

Question 14

If the graph of $y = f(x)$ has a vertical asymptote at $x = -4$, what is the domain of $f(x)$?

Accepted Answer

$(-\infty, -4) \cup (-4, \infty)$

Question 15

Which interval describes where the function $y = f(x)$ is decreasing, given the graph with decreasing intervals $(0, 2)$?

Accepted Answer

$(0, 2)$

Question 16

Given the graph of $y = f(x)$, what is the range if the lowest point is $y = -3$ and the highest is $y = 0$?

Accepted Answer

$[-3, 0]$

Question 17

If $f(x)$ has a relative minimum at $x = -3$ and $x = 5$, which of the following is true?

Accepted Answer

$f(x)$ changes from decreasing to increasing at $x = -3$ and $x = 5$.

Question 18

Which of the following is the correct definition of a y-intercept?

Accepted Answer

The y-coordinate of the point where the graph crosses or touches the y-axis.

Question 19

Given $f(x) = x^2 - 2x - 2$, which of the following is true about its intercepts?

Accepted Answer

It has two x-intercepts and one y-intercept.

Intercepts, Domain & Range, Asymptotes, and Behavior of Functions: College Algebra Study Notes

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