Question 1

Remember: When there is a number being added or subtracted in the denominator of a rational expression, what transformation does that cause?

Accepted Answer

Shift Left or Right

Answer

Shift Up or Down

Answer

Vertical Stretch or Compression

Answer

Reflection

Question 2

Comprehend: Compare the two rational functions based on their transformations. $f(x)=\frac{1}{x}+5$   and   $g(x)=\frac{1}{x}-5$

Accepted Answer

$f(x)$ is shifted up 5, while $g(x)$ is shifted down 5

Answer

$f(x)$ is shifted down 5, while $g(x)$ is shifted up 5

Answer

$f(x)$ is shifted right 5, while $g(x)$ is shifted left 5

Answer

$f(x)$ is shifted left 5, while $g(x)$ is shifted right 5

Question 3

Comprehend: Compare the difference between a vertical and horizontal translation with regards to the asymptotic behavior of a rational function.

Accepted Answer

A vertical translation causes the Horizontal Asymptote to change. A horizontal translation causes the Vertical Asymptote to change.

Answer

There are no asymptotes in Rational functions

Answer

A vertical translation causes the Vertical Asymptote to change. A horizontal translation causes the Horizontal Asymptote to change.

Answer

Translations don't affect Asymptotes, only stretches and compressions do.

Question 4

Apply: Given the rational function, list the transformations from its parent function. $g(x)=\frac{-2}{x+3}-2$

Accepted Answer

Vertical Stretch by 2,  Reflection across x-axis, left 3, down 2

Answer

Vertical Stretch by 2, Reflection across x-axis, right 3, down 2

Answer

Vertical Compression by 2,  left 3, down 2, Reflection across x-axis

Answer

Vertical Stretch by 2,  left 3, down 2

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