Quiz about Graphing and Transformations of Rational Functions Refresher

Question 1

What is the form of a rational function?

Accepted Answer

f(x) = $$\frac{p(x)}{q(x)}$$

Answer

f(x) = p(x) + q(x)

Answer

f(x) = p(x) imes q(x)

Answer

f(x) = p(x) - q(x)

Question 2

An asymptote is a line that a graph approaches but never ________.

Accepted Answer

A) touches

Answer

B) crosses

Answer

C) meets

Answer

D) intersects

Question 3

The horizontal asymptote of the function $$f(x) = \frac{a}{x-h} + k$$ is at $$y =$$ ________.

Accepted Answer

B) $$k$$

Answer

A) $$h$$

Answer

C) $$a$$

Answer

D) $$0$$

Question 4

What is the horizontal asymptote of the reciprocal function $$f(x) = \frac{1}{x}$$ ?

Accepted Answer

B) $$y = 0$$

Answer

A) $$x = 0$$

Answer

C) $$x = 1$$

Answer

D) $$y = 1$$

Question 5

What does $$|a| > 1$$ indicate about the graph of $$f(x) = \frac{a}{x-h} + k$$ ?

Accepted Answer

A) Vertical stretch

Answer

B) Vertical compression

Answer

C) Horizontal stretch

Answer

D) Horizontal compression

Question 6

What is the graph of $$f(x) = \frac{1}{x}$$ known as?

Accepted Answer

Hyperbola

Answer

Parabola

Answer

Ellipse

Answer

Circle

Question 7

What is the range of $$f(x) = \frac{1}{x}$$ in interval notation?

Accepted Answer

$$\left(-\infty,0\right)\ \cup\left(0,\infty\right)$$

Answer

$$y<0\ OR\ y>0$$

Answer

All real Numbers except y=0

Answer

All real Numbers expect x=0

Question 8

Fill in the blank: The domain of the function $$f(x) = \frac{1}{x+3} - 2$$ is all real numbers except ____.

Accepted Answer

x = -3

Answer

x = 3

Answer

x = 2

Answer

x = -2

Question 9

What is the range of the function $$f(x) = \frac{-2}{x-2} + 4$$ ?

Accepted Answer

All real numbers except y = 4

Answer

All real numbers

Answer

All real numbers except y = -4

Answer

All real numbers except y = 2

Question 10

What is the first step in graphing the function $$f(x) = \frac{1}{x+3} - 2$$ ?

Accepted Answer

Determine the x and y Asymptotes

(Vertical and Horizontal Asymptotes)

Answer

Graph both Asymptotes

Answer

Calculate the y-values

Answer

List the Domain and Range

Question 11

Fill in the blank: The horizontal asymptote of the function f(x) = $$\frac{1}{x+3} - 2$$ is ____.

Accepted Answer

y = -2

Answer

y = 2

Answer

y = 3

Answer

y = -3

Question 12

In which step do you draw the two branches making sure not to touch the asymptotes?

Accepted Answer

Step 5

Answer

Step 3

Answer

Step 4

Answer

Step 6

Question 13

What is the horizontal asymptote of the function $$f(x) = \frac{-2}{x-2} + 4$$ ?

Accepted Answer

y = 4

Answer

y = -4

Answer

y = 2

Answer

y = -2

Question 14

Fill in the blank: The range of the function $$f(x) = \frac{1}{x+3} - 2$$ is all real numbers except ____.

Accepted Answer

y = -2

Answer

y = 2

Answer

y = 3

Answer

y = -3

Question 15

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

Accepted Answer

All real numbers except x = 2

Answer

All real numbers

Answer

All real numbers except x = -2

Answer

All real numbers except x = 4

Question 16

What is the first step in graphing the function $$\frac{x^2+2x-3}{x-2}$$ ?

Accepted Answer

Determine the x and y Asymptotes

(Vertical and Horizontal Asymptotes)

Answer

Graph both Asymptotes

Answer

Calculate the y-values

Answer

List the Domain and Range

Question 17

What is the formula for finding the x-intercepts of a rational function?

Accepted Answer

Set the numerator equal to 0 and solve for x

Answer

Set the denominator equal to 0 and solve for x

Answer

Plug 0 into the simplified function and solve for y

Answer

Compare the degrees of the numerator and denominator.

Question 18

Which of the following is true about horizontal asymptotes?

Accepted Answer

They describe end behavior

Answer

They occur where the numerator is zero

Answer

They are points where the graph crosses the axes

Answer

They are points where the function is undefined.

Question 19

Which of the following is used to find the y-intercepts of a rational function?

Accepted Answer

Plug 0 into the simplified function

Answer

Set the numerator equal to 0

Answer

Set the denominator equal to 0

Answer

Compare the degrees of the numerator and denominator.

Question 20

Fill in the blank: A rational function often has a vertical asymptote where the ______ is zero.

Accepted Answer

denominator

Answer

numerator

Answer

x-intercept

Answer

y-intercept

Question 21

Fill in the blank: To find the x-intercepts, set the ______ equal to 0 and solve for x.

Accepted Answer

numerator

Answer

denominator

Answer

simplified function

Answer

original function

Question 22

Fill in the blank: A rational function has a horizontal asymptote of $$y=0$$ if the degree of the numerator is ______ the degree of the denominator.

Accepted Answer

B) less than

Answer

A) greater than

Answer

C) equal to

Answer

D) not equal to

Question 23

What is the vertical asymptote of the function f(x) = (x-2)/(x-1)(x+3)?

Accepted Answer

x = 1

Accepted Answer

x = -3

Answer

x = 2

Answer

x = 0

Question 24

What is the vertical asymptote of the function f(x) = $$\frac{x^2+2x-3}{x-2}$$ ?

Accepted Answer

x = 2

Answer

x = -2

Answer

x = 3

Answer

x = -3

Question 25

Find the hole

$$y=\frac{x+2}{x^{2\ }+7x+10}\ $$

Accepted Answer

$$\left(-2,\ \frac{1}{3}\right)$$

Answer

$$\left(2,\frac{1}{7}\right)$$

Answer

$$\left(-2,3\right)$$

Answer

$$\left(2,7\right)$$

Question 26

Identify the hole in the function

$$y=\frac{x-3}{x^{2}-5x+6}\ $$

Accepted Answer

$$\left(3,1\right)$$

Answer

$$\left(3,\frac{1}{3}\right)$$

Answer

$$\left(2,\ \frac{1}{2}\right)$$

Answer

$$\left(2,3\right)$$

Question 27

How is this function transformed from the parent function?

Accepted Answer

Translated right and down

Answer

Translated left and up

Answer

Translated right and up

Answer

Translated left and down

Question 28

What is the domain and range?

Accepted Answer

$$D:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$$

$$R:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$$

Answer

$$D:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$$
$$R:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$$

Answer

$$null$$
$$R:\ \left(-\infty,\frac{1}{2}\right)\cup\left(\frac{1}{2},\infty\right)$$

Answer

$$D:\ \left(-\infty,-2\right)\cup\left(-2,\infty\right)$$
$$R:\ \left(-\infty,-1\right)\cup\left(-1,\infty\right)$$

Question 29

Describe the transformations from the parent function, f(x) = 1/x.

Accepted Answer

Shift right 9 units, shift up 2 units

Answer

Shift left 9 units, shift up 2 units

Answer

Shift right 9 units, shift down 2 units

Answer

Shift right 2 units, shift down 9 units

Question 30

What is an asymptote?

Accepted Answer

an imaginary line that your function never touches

Answer

a part of your function

Answer

a point on your graph

Answer

a type of fruit

Question 31

What is the domain of a rational function?

Accepted Answer

All real numbers except the vertical asymptote

Answer

All real numbers except the horizontal asymptote

Question 32

What is the range of a rational function?

Accepted Answer

All real numbers except the horizontal asymptote

Answer

All real numbers except the vertical asymptote

Question 33

What is the equation for the horizontal asymptote?

Accepted Answer

$$y=$$

Answer

$$x=$$

Question 34

What is the equation for the vertical asymptote?

Accepted Answer

$$x=$$

Answer

$$y=$$

Question 35

If the original function is f(x), how will -f(x) transform f(x)?

Accepted Answer

Reflection of f(x) across the x-axis

Answer

One way stretch, parallel to x-axis, with scale factor 1/a

Answer

One way stretch, parallel to y-axis, with scale factor a

Answer

Translation of f(x) with vector (t , s)

Answer

Reflection of f(x) across the y-axis

Graphing and Transformations of Rational Functions Refresher

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