Asymptotes Algebraically

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

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What is/are the vertical asymptote(s)?

• There are no vertical asymptotes

• x=5

• x=-5

• x=-1/2

What is the hole?

• x= 4

• x= -4

• x= 5

• x= -5

The function below has a horizontal asymptote. Find the equation of this horizontal asymptote.

The function below has a horizontal asymptote. Find the equation of this horizontal asymptote. Equation of Horizontal Asymptote: y=____________

The function below has a horizontal asymptote. Find the equation of this horizontal asymptote. f\left(x\right)=\frac{3x-6}{4x^2-2x+10} Equation of Horizontal Asymptote: y=____________

• x = 2

• x = -2

• x = 2 & -2

• This function does not have any vertical asymptotes

• x = 2

• x = 0

• x = 4 & -1

• This function does not have any vertical asymptotes

Algebraically, we can find the vertical asymptotes of rational functions by...

• finding what makes the denominator equal to zero.

• finding what makes the common factors cancelled out equal to zero.

State the vertical asymptote for the following function: