Rational Function Discontinuity

Which of the following could be f(x)?

• Only x = 2

• Only x = -2

• Only x = 3

• x = 2 and x = 3

• x = -2 and x = 3

Determine the hole(s) for the following function. f\left(x\right)=\frac{\left(x+3\right)}{\left(x-5\right)\left(x+3\right)}

• x = -3

• x = 5

• x = -3 and x = 5

• x = 0

• Does Not Exist

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: y = 0

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 0

• Holes: Do Not Exist
  Vertical: x = 1/2 and x = -4
  Horizontal: y = 1

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 1

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: Does Not Exist

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

• 
• 
• 
• 

The domain of a rational function is restricted by ALL factors in the denominator. These factors show up as removable and infinite points of discontinuity on the graph known as ...

• Holes

• Vertical Asymptotes

• Horizontal Asymptotes

• Jumps

What is the x-intercept, vertical asymptote, hole, and domain?

A removable point of discontinuity is a factor that can be canceled out from the rational function. It shows up as an open circle on the graph. Its called a...

• holes

• vertical asymptotes

• x-intercepts

• points

Infinite discontinuity is found from the factor(s) left in the denominator after simplifying. It shows up as a break in the graph called a...

• holes

• vertical asymptotes

• x-intercepts

• points

Why do rational functions have domain restrictions?

• Can't divide by zero!

• The sky is blue

• It's always zero.

• There are holes and asymptotes.