Rational Functions Removable Discontinuities

Determine the type(s) and location(s) of all discontinuities

• jump at x = -3, infinite at x = 2, removable at x = 2.

• jump at x = -3, removable at x = 2, removable at x = 4.

• removable at x = -3, removable at x = 2, removable at x = 4.

• jump at x = -3, removable at x = 2, jump at x = 4.

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

What can be my first step to find the discontinuities of the function?

• Factor the numerator and denominator

• Cancel the x²

• Plug in zero

When does the denominator of the factored function equal zero? (select all that apply)

• x= -5

• x= 2

• x= 5

• x= -2

• x= 6

Polly was given the rational function shown. f\left(x\right) = \frac{x+3}{x^2+x-6}+4 What discontinuities did Polly discover upon her investigation of this function?

• x=2

• x= -3

• x= 4

• x=3

• x= -2

• removable

• x=2

• jump

• infinite

• x= -2

• x=5

• x= -5

Polly was given the rational function shown. f\left(x\right) = \frac{x+3}{x^2+x-6}+4 What discontinuities did Polly discover upon her investigation of this function?

• x=2

• x= -3

• x= 4

• x=3

• x= -2

The function has a (n)​ (a)   discontinuity at ​ (b)  

• removable

• x=3

• infinite

• jump

• x=-3

• x=-6

• x=9

• x=2

• x=5

Tags

continuity

What is the hole?

• x= 4

• x= -4

• x= 5

• x= -5

Identify the Discontinuities

• Vertical Asymptote at x=1

• Hole at x=-1

• Vertical Asymptote at x=-1

• Hole at x=1