6.3 Graphing Rational Functions

6.3 Graphing Rational Functions

This will review the notes you took on 6.3. There are new examples so you may want to take some additional notes on notebook paper!

Multiple Select

Does the rational function have any discontinuities? $$y=\frac{x^2-3x-4}{x-2}$$  Select all that apply. 

• $$x=2$$  is a hole

• $$x=2$$  is a vertical asymptote

• $$x=4$$  is a vertical asymptote

• $$x=-1$$  is a vertical asymptote

Multiple Select

Does the rational function have any discontinuities? $$y=\frac{2x+2}{x^2-1}$$ Select all that apply. 

• $$x=1$$  is a hole

• $$x=1$$  is a vertical asymptote

• $$x=-1$$  is a hole

• $$x=-1$$  is a vetical asymptote

Multiple Choice

Where are the holes in the rational function below? $$y=\frac{3x^2+15x+18}{x^2+4x-5}$$ Select all that apply.  

• $$x=-5$$  is a hole

• $$x=1$$  is a hole

• $$x=3$$  is a hole

• there are no holes in this function

Multiple Select

How many y-intercepts can a rational function have? (Select all that apply)

• 0

• 1

• 2

• many

Multiple Choice

What is the y-intercept of the rational equation?  $$y=\frac{x-4}{2-x}$$  

• (0,-2)

• (0,4)

• (0,2)

• (0,-4)

Multiple Select

What are the x-intercepts of the rational expression below.  $$y=\frac{2x^2+7x+3}{x^2+4x+2}$$   Select all that apply. 

• $$(0,0)$$  

• $$(-3,0)$$  

• $$\left(\frac{1}{2},0\right)$$  

• $$\left(-\frac{1}{2},0\right)$$  

Multiple Choice

Which of the following does not have a horizontal asymptote?

• $$y=\frac{2x^3+7x^2+3x}{x^2+4x+4}$$

• $$y=\frac{x-3}{x^2+x-12}$$

• $$y=\frac{x-4}{2-x}$$

• they all have a horizontal asymptote

Multiple Choice

What is the horizontal asymptote of the rational equation below? $$y=\frac{3x^2+15x+18}{x^2+4x-5}$$  

• $$y=\frac{1}{3}$$  

• $$y=3$$  

• $$y=0$$  

• $$y=1$$  

Multiple Choice

What is the horizontal asymptote of the graph of rational equation below?  $$y=\frac{x-12}{x^2+2x-3}$$  

• $$y=0$$  

•   $$y=1$$  

• $$y=4$$  

• $$y=\frac{1}{2}$$  

Multiple Choice

Which of the following has a slant (oblique) asymptote?

• $$y=\frac{x^2-3x-4}{x-2}$$  

• $$y=\frac{3}{x^2-1}$$  

• $$y=\frac{x-3}{x^3+x^2-12}$$  

Multiple Choice

What is the equation of the slant asymptote of the rational equation below? $$y=\frac{2x^3+7x^2+3x}{x^2+4x+4}$$  

• $$y=2x-1$$  

• $$y=-2x+1$$  

• $$y=-9x-4$$  

• $$y=2$$  

Thank you for finishing this lesson!

If you have any questions, please your teacher know! You can go back through this again if you would like to improve your score.

Please review your notes from 6.3 and make sure you have finished practice problems 1-12 so we can being graphing.