Removable Asymptotes

Identify the type of location of the discontinuity/discontinuities.

• Removable at x = 5 ; Infinite at x = -1

• Removable at x = -5 ; Infinite at x = 1

• Infinite at x = 1

• Infinite at x = 2

Where is the removable discontinuity?

• x=2

• x=2 and x=3

• x=-3

• x=3

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.

What is the hole?

• x= 4

• x= -4

• x= 5

• x= -5

Determine whether the graph of the function has a vertical asymptote or a removable discontinuity (hole) at x = -1.

• Vertical Asymptote

• Discontinuity

• Neither

What are the domain and range of the graph?

• Domain: All real numbers

  Range: All real numbers

Which statement represents the type(s) of discontinuity for the rational function?

• The function has a removable discontinuity at x = 3 and x = –3.

• The function has a vertical asymptote at x = 3 and x = –3

• The function has a non-removable discontinuity at x = –3 and a vertical asymptote at x = 3.

• The function has a removable discontinuity at x = 3 and a vertical asymptote at x = –3.

• None
• x = 2
• x = 3
• x = 4

In f(x) = x² + 5x + 6 ∕  x + 3, at what value of x it will be a removable discontinuity?

• -3

• -2

• 2

• 3

Where is the hole in this graph?

• x = -3

• x = 3

• x = 5

• None