Simple Rational Function Transformations

Summary of Rational Root Parent Functions and Transformation with Asymptotes

Multiple Choice

What varies inversely with the length of the string on a stringed instrument?

• the frequency of the sound wave

• the constant of variation, k

• the frequency of the vibrations of the string

• the length of the instrument in centimeters

Fill in the Blanks

Multiple Select

For the transformed rational function f(x) =

$$\frac{5}{x-4}-3$$  
Find the h and k values and the domain and range. Check the correct boxes.

• 
  
  
  
  h = -4, k = 3
  
  
  
  
  

• h = 4, k = -3

• h = 5, k = -3

• D : x $$\ne$$  -4
  R:  y  $$\ne$$  3

• D: x  $$\ne$$  4
  R: y  $$\ne$$  -3

 $The\ transformed\ function\ has\ the\ form\ f\left(x\right)\ =\frac{a}{x\ -\ h}+\ k$  

Fill in the Blanks

Multiple Select

Check all that apply:
In the function f(x) =

$$\frac{5}{x}$$  the 5 is the...

• constant of variation, k

• the constant of proportionality

• the a in the transformations form

• the vertical stretch by a factor of 5 of the parent function

• a horizontal stretch by a factor of 5

Inverse Variation

has the form 

 $y\ =\frac{k}{x}$  

Multiple Choice

True or False:  Every rational function has an excluded value(s). Think about the function f(x) =

$$\frac{x-4}{x^2+\ 4}$$  

• True

• False