Rational Function Asymptotes and Holes

Find the vertical asymptote.
g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• To finish finding the coordinates of a hole, place the x value in the reduced equation

Identify the x-value of the hole(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

The horizontal asymptote equals zero when:

• Slant asymptote

• the degree of the numerator is exactly one degree more than the demoninator

• y=0

• the degree of the numerator is less than the degree of the denominator

• None

• the degree of the numerator and denominator are equal

• divide the coefficients

• the degree of the numerator is greater than the degree of the denominator

• y=0

• the degree of the numerator is less by one or more of the denominator

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = 2

• No Hole

• Horizontal Asymptote is y = -1/3

• x-intercept is (3, 0)

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = 1

• No Holes

• Horizontal Asymptote is y = 0

• No Horizontal Asymptote

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = -4

• No Holes

• Horizontal Asymptote is y = -1/4

• No Horizontal Asymptote

• Vertical Asymptote is x = 4

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = -3

• Hole at (1, -2)

• Horizontal Asymptote is y = 2

• No Horizontal Asymptote

• Vertical Asymptote is x = 3

Select ALL that apply.

• There is a hole at (-5, -3)

• The vertical asymptote is x=0

• The horizontal asymptote is at y=0

• There is no horizontal asymptote.

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