Quiz about Transformations with Rational Functions

Question 1

Describe the transformations of the function.

Accepted Answer

Shift up by 2 units

Reflected over the x-axis

Answer

Shift down by 2 units

Reflected over the y-axis

Answer

Shift up by 2 units

Reflected over the y-axis

Answer

Shift left by 2 units

Reflected over the x-axis

Question 2

What is the horizontal asymptote?

Accepted Answer

y = 7

Answer

x = 2

Answer

x = 7

Answer

y = 2

Question 3

Describe the transformation from the rational parent function to function f: f\left(x\right)=\frac{1}{x+2}-1

Accepted Answer

shift down 1, left 2

Answer

shift up 1, right 2

Answer

shift up 1, left 2

Answer

shift down 1, right 2

Question 4

Describe the transformation from the rational parent function to the function g (check all boxes that apply): g(x)= \frac{2}{x-3}+5

Accepted Answer

vertical stretch by a factor of 2

Accepted Answer

shift right 3

Accepted Answer

shift up 5

Answer

shift left 3

Answer

vertical reflection

Question 5

How is this function transformed from the parent function f(x) = 1/x?

Accepted Answer

Reflected over the x-axis

Translated up by 2 units

Answer

Reflected over the y-axis

Translated down by 2 units

Answer

Reflected over the y-axis

Translated up by 2 units

Answer

Reflected over the x-axis

Translated left by 2 units

Question 6

How is this function transformed from the parent function ?

Accepted Answer

Translated Right 5 and Down 1

Answer

Translated Right 5 and Up 1

Answer

Translated Left 5 and Up 1

Answer

Translated Left 5 and Down 1

Question 7

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

Accepted Answer

Translate right 9 units, shift up 2 units

Answer

Translate left 9 units, shift up 2 units

Answer

Translate right 9 units, shift down 2 units

Answer

Translate right 2 units, shift down 9 units

Question 8

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 9

Which rational function has been compressed by a factor of 1/4, reflected across the x-axis, shifted to the left 3 units, and shifted down 5 units.

Accepted Answer

$$y=\frac{-1}{4\left(x+3\right)}-5$$

Answer

$$y=\frac{1}{4\left(x-5\right)}+3$$

Answer

$$y=\frac{-1}{\left(x+5\right)}+3$$

Answer

$$y=\frac{-1}{\left(x-3\right)}-5$$

Question 10

Suppose you translate the graph of $$y=\frac{3}{x}$$ so that the new graph has asymptotes at x= -5 and y=14. What is the equation for the new graph?

Accepted Answer

$$y=\frac{3}{x+5}+14$$

Answer

$$y=\frac{3}{x-5}-14$$

Answer

$$y=\frac{3}{x-14}-5$$

Answer

$$y=\frac{3}{x+14}+5$$

Question 11

Describe the transformations from the parent function katex latex="y=\frac{1}{x}"

Accepted Answer

Left 5 and Up 7

Answer

Right 5 and Up 7

Answer

Left 7 and Up 5

Answer

Right 5 and Down 7

Question 12

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 13

A rational function is shifted to the right 2 units and shifted up 4 units. Which is a possible equation?

Accepted Answer

$$y=\frac{1}{x-2}+4$$

Answer

$$y=\frac{1}{x+4}+2$$

Answer

$$y=\frac{1}{x-4}+2$$

Answer

$$y=\frac{1}{x+2}+4$$

Question 14

Describe the transformation from the rational parent function to the function f (check all boxes that apply):

Accepted Answer

vertical reflection

Accepted Answer

vertical stretch by a factor of 5

Accepted Answer

shift down 3

Accepted Answer

shift left 4

Answer

shift right 4

Question 15

Describe the transformation from the rational parent function to the function f (check all boxes that apply): f(x)=-5-\frac{4}{x+1}

Accepted Answer

shift left 1

Accepted Answer

shift down 5

Accepted Answer

vertical stretch by a factor of 4

Accepted Answer

vertical reflection

Answer

shift right 5

Question 16

What transformations has the function undergone?

Accepted Answer

reflect over x, vertical stretch by 2, right 5, up 1

Answer

reflect over y, vertical compression by 2, right 5, up 1

Answer

reflect over x, vertical compression by 2, left 5, up 1

Answer

reflect over y, vertical stretch by -2, right 5, up 1

Question 17

The function g(x), shown on the graph, was obtained by translating the graph of $$f\left(x\right)=\frac{1}{x}$$ . Which description best describes the transformations performed on to obtain ?

Accepted Answer

Translation left 2 and down 4

Answer

Translation right 2 and up 4

Answer

Translation left 2 and up 4

Answer

Translation right 2 and down 4

Question 18

Question 18.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 19

Describe all transformations from the rational parent function g(x)=1/x to the given function f(x)

Accepted Answer

Shift left 5 and shift up 7

Answer

Shift right 5 and shift up 7

Answer

Shift left 7 and shift up 5

Answer

Reflect over the x-axis, shift up 7

Question 20

How was the parent function shifted to obtain this graph?

Accepted Answer

4 units left and 3 units up

Answer

3 units left and 4 units up

Answer

4 units right and 3 units down

Answer

3 units right and 4 units down

Transformations with Rational Functions

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