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

Guida di studio - Domande di pratica

Study guide - Flashcard