Asymptotes and Discontinuities

Skill Check: Rational Function Transformations and Discontinuities.

Today

• Get a piece of scratch paper. You will not be able to do a good job/get a score without writing out your work.

• Seriously, get up and get scratch paper.

• Do your best! You may retake the quiz as many times as you want. Good luck! - Shin

Multiple Choice

What is the name of this function?

• Quadratic Function

• Rational Function 

• Absolute Value Function 

• Cubic Function

Multiple Choice

Describe the transformations from the parent function g(x) = 1/x

• vertical compression by 3, right 7

• vertical stretch by 3, right 7

• vertical stretch by 3, up 7

• vertical compress by 1/3, up 7

Multiple Choice

Describe all transformations from the parent function g(x)=1/x to f(x).

• Shift right 5 and shift up 7

• Shift left 7 and shift up 5

• Reflect over the x-axis, shift up 7

• Shift left 5 and shift up 7

Multiple Choice

Describe the transformations from the parent function g(x) =1/x

• reflection over the x-axis, right 2, down 4

• reflection over the y-axis, right 2 down 4

• reflection over the x-axis, left 2, down 4

• reflection over the y-axis, left 2, down 4

Multiple Choice

Find the Vertical Asymptote(s) for the following function

$$g\left(x\right)\ =\frac{x-9}{\left(x-4\right)\left(x+2\right)}$$  

• $$x=-4,\ x=2$$  

• $$x=-2,\ x=4$$  

• $$x=-6,\ x\ =\ -2$$  

• $$x=\ 2,\ x=6$$  

Multiple Choice

Find the hole(s) for the following function

$$g\left(x\right)\ =\frac{x-9}{\left(x-4\right)\left(x+2\right)}$$  

• $$x=-4$$  

• $$x=-2$$  

• $$x=9$$  

• There are no holes in g(x). 

A NOTE FROM SHIN:

Hi all,

Follow along with the following slides and do your best on the questions related to Horizontal Asymptotes. Do your best, but you will not be penalized if you miss questions specifically related to Horizontal Asymptotes (because of the College of Alameda field trip).

• Shin

Finding Horizontal Asymptotes

Finding Horizontal Asymptotes

Finding Horizontal Asymptotes

Multiple Choice

What is the horizontal asymptote of the following function?

$$f\left(x\right)=\frac{3x^2}{4x^2-1}$$  

• $$y=\frac{3}{4}$$  

• $$y=\frac{4}{3}$$  

• $$y=0$$  

• No asymptote

Multiple Choice

What is the horizontal asymptote for the following function?

$$f\left(x\right)=\frac{4x+3}{x^2-4}$$  

• $$y=4$$  

• $$y=\frac{1}{4}$$  

• $$y=0$$  

• No Asymptote

Multiple Choice

To find holes and vertical asymptotes, you factor the given function and look for values that make the bottom of the function equal to zero.

• TRUE

• FALSE

Multiple Choice

Find the vertical asymptotes of the function:

$$f\left(x\right)=\frac{x^2+2x-3}{x^2-5x+6}$$  

• $$x=2,3$$  

• $$x=-3,-2$$  

• $$x=-3,1$$  

• None

Multiple Choice

Find the vertical asymptotes of the function:

$$f\left(x\right)=\frac{x-27}{x^2+10x+9}$$  

• $$x=-9,-1$$  

• $$x=1,9$$  

• $$x=3$$  

• None