Rational Function Transformations

Rational Function Transformations

SLT 23: Identify the effect of transformations on the graph of a rational function

​Graphing Rational

functions​

Open Ended

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Transformations of Rational Functions

Recall the two parent functions from our last class (page 11 and page 14) and your NearPod assignment.

​Now recall the transformation rules you learned during first semester.

TRANSFORMATION RULES

​Now lets put those two concepts togethers

• Vertical dilation by a factor of 2

• Horizontal translation right 3

• Vertical translation up 4

• Horizontal translation right 2

• Vertical translation down 3

Multiple Choice

Given

$$y=\frac{2}{x-5}+3$$   Determine the Horizontal Asymptote

• $$y=2$$  

• $$y=0$$  

• $$y=3$$  

• $$y=5$$  

Fill in the Blank

Given

$$y=\frac{3}{x+7}+6$$  
Identify the horizonal asymptote

Fill in the Blank

Given

$$y=\frac{3}{x+7}+6$$  
Identify the vertical asymptote

Multiple Choice

What are the asymptotes?

• x=-3, y=1

• x=3, y =1

• x=-3, y =-1

• x=3 y=-1

Multiple Choice

Given

$$y=\frac{3}{\left(x-4\right)^2}-5$$  Determine the Vertical and Horizontal Asymptotes

• $$x=3\$$  and  $$y=5$$  

• $$x=4$$  and  $$y=-5$$  

• $$x=-4$$  and  $$y=5$$  

• $$x=-4$$  and  $$y=-5$$  

Multiple Choice

Given

$$y=\frac{3}{\left(x-4\right)^2}-5$$  Determine the Domain and Range

• $$D:\left(-\infty,4\right)\cup\left(4,\infty\right)$$  and  $$R:\left(5,\infty\right)$$  

• $$D:\ \left(-\infty,4\right)\cup\left(4,\infty\right)$$  and  $$R:\left(-5,\infty\right)$$  

• $$D:\ x=-4$$  and  $$R:y=5$$  

• $$D:\ x<-4$$  and  $$R:y>-5$$  

Multiple Choice

Which asymptote(s) are determined by looking at the denominator?

• Horizontal Asymptote

• Vertical Asymptote

• Both

Multiple Choice

How is this function transformed from the parent function ?

$$y=\frac{1}{x}$$  

• Translated Right 5 and Up 1

• Translated Right 5 and Down 1

• Translated Left 5 and Up 1

• Translated Left 5 and Down 1

Multiple Choice

Describe the transformations from the parent function

$$y=\frac{1}{x}$$  

• Right 5  and  Up 7

• Left 7  and  Up 5

• Reflect over the x-axis  and  Up 7

• Left 5  and  Up 7

Poll

Do you understand how to describe the transformations

• Yes

• No

• Kinda

Poll

Do you understand how to determine the key features?

• Yes

• No

• Kinda