Quiz about Transformations of Rational Functions

Question 1

What is the transformation of: $$f\left(x\right)\ =\ \frac{2}{x+1}$$

Accepted Answer

Stretch of 2 and Left 1

Answer

Compression of 2 and Left 1

Answer

Stretch of 2 and Right 1

Answer

Compression of 2 and Right 1

Question 2

Describe all transformations from the parent function g(x)=1/x to 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 3

Describe the transformations from the parent function g(x) = 1/x

Accepted Answer

vertical stretch by 3, up 7

Answer

vertical compression by 3, right 7

Answer

vertical stretch by 3, right 7

Answer

vertical compress by 1/3, up 7

Question 4

What is the horizontal asymptote?

Accepted Answer

y = 7

Answer

x = 2

Answer

x = 7

Answer

y = 2

Question 5

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 6

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 7

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 8

Referring to f(x) = $$\frac{1}{x}$$ how does f(x) = $$\frac{1}{x+2}-5$$ translate?

Accepted Answer

Shifts left 2 units and down 5 units.

Answer

Shifts left 2 units and up 5 units.

Answer

Shifts right 2 units and up 5 units.

Answer

Shifts right 2 units and down 5 units.

Question 9

Describe the transformations from the parent function

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 10

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 11

Referring to f(x) = $$\frac{1}{x}$$ how does f(x) = $$\frac{1}{x-4}+1$$ Translate.

Accepted Answer

Shifts right 4 units and up 1 unit.

Answer

Shifts left 4 units and up 1 unit.

Answer

Shifts left 4 units and down 1 unit.

Answer

Shifts right 4 units and down 1 unit.

Question 12

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 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 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 15

Determine the excluded value.

Accepted Answer

x = -6

Answer

x = 6

Answer

x = 0

Answer

x = -6, 9

Question 16

Describe the transformation.

Accepted Answer

Reflect over x-axis, left 3, up 3

Answer

Reflect over x-axis, right 3, up 3

Answer

Reflect over y-axis, left 3, up 3

Answer

Reflect over x-axis, right 3, down 3

Question 17

Describe the transformation

Accepted Answer

vertical stretch by a factor of 2, right 2, down 2

Answer

vertical stretch by a factor of 2, left 2, up 2

Answer

vertical stretch by a factor of 2, right 2, up 2

Answer

vertical compression by a factor of 2, right 2, down 2

Question 18

What is the vertical asymptote?

Accepted Answer

x = 2

Answer

y = 2

Answer

x = 1

Answer

y = 1

Question 19

For which value is the expression undefined?

Accepted Answer

3

Answer

-4

Answer

-3

Answer

0

Question 20

How is this rational function transformed from the parent function: $$y=\frac{3}{x}$$

Accepted Answer

Stretched by a factor of 3

Answer

Compressed by a factor of 3

Answer

Shifted up by 3

Answer

Shifted down by 3

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