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 Blank

The frequency of cycles per second of vibration when the length of the string is 10 inches is...

Fill in the Blank

In the rational parent function, where h = 0 and k = 0 the asymptotes are x =____ and y = ______

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 Blank

In the above rational function the vertical asymptote is x = _____ and the horizontal asymptote is y = ________

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 

 $y\ =\frac{k}{x}$  

Fill in the Blank

What is the excluded value for the function:
f(x) =

$$\frac{x+6}{x\ -\ 5}$$  

Recall that the excluded value(s) are those values that would cause you to divide by zero and that is not possible!

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