Domain and Discontinuities of Functions

Domain and Discontinuities of Functions

Find the "problem" or what could affect your domain

Multiple Select

What can you look for in the function that can affect your domain?

• Possible Zeros in the denominator

• Possible negatives in the radicals (even roots)

• Zeros in the Numerator

• Polynomials with fractions

• Constants

Elements of a function that affect the domain

• Zeros in the denominator

• Negatives inside of an even root

Multiple Select

What type of discontinuities can occur in a rational function?

• A hole in the graph

• An asymptote

• A jump

• Rational functions are always continuous

A rational function can cause

Both an asymptote or a hole in the graph, depending on how the zeros appear.

Multiple Choice

If the zero in the denominator can be cancelled (crossed out) it creates...

• A hole in the graph

• A vertical asymptote

• A parabola

Multiple Choice

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

• vertical
• horizontal
• slant
• none

Multiple Choice

Where is the Vertical Asymptote of this function?

• x= -5

• x= 5

• x= 6

• x= -6

Multiple Choice

What is my first step to find the discontinuities for this function?

• Factor the numerator and denominator

• Plug in zero

• Cancel the x² on the numerator and denominator

Multiple Choice

Where is the hole in this function?

• x= 4

• x= -4

• x= 5

• x= -5

 $\frac{\left(x^2-25\right)}{x^2-x-20}=\frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+4\right)}$  

Multiple Choice

What are the Vertical Asymptotes of...

• x = 0, -5

• x=0, 5

• x = 2, -7

• x = -2, 7

 $\frac{-3\left(x-2\right)\left(x+7\right)}{x^2+5x}=\frac{-3\left(x-2\right)\left(x+7\right)}{x\left(x+5\right)}$  

Multiple Choice

What is/are the vertical asymptote(s)?

• There are no vertical asymptotes
• x=5
• x=-5
• x=-1/2

 $\frac{2x^2-9x-5}{x-5}=\frac{\left(x-5\right)\left(2x+1\right)}{x-5}$