Graphs of Rational Functions

How do you find the vertical asymptotes?

• Set the simplified denominator equal to zero and solve.

• Set the canceled out parts of the denominator equal to zero and solve.

• Set the simplified numerator equal to zero and solve.

• Use the leading terms only from the top and bottom and simplify.

• Divide the polynomial on the top by the polynomial on the bottom.

Tags

CCSS.HSF-IF.C.7D

How do you find the horizontal asymptote?

• Set the simplified denominator equal to zero and solve.

• Set the canceled out parts of the denominator equal to zero and solve.

• Set the simplified numerator equal to zero and solve.

• Examine the degree of the numerator and denominator.

• Divide the polynomial on the top by the polynomial on the bottom.

Tags

CCSS.HSF-IF.C.7D

How do you find the slant asymptote?

• Set the simplified denominator equal to zero and solve.

• Set the canceled out parts of the denominator equal to zero and solve.

• Set the simplified numerator equal to zero and solve.

• Use the leading terms only from the top and bottom and simplify.

• Long division of the polynomial on the top by the polynomial on the bottom.

Tags

CCSS.HSF-IF.C.7D

When will a slant asymptote exist?

• When the degree of the top is BIGGER than the degree of the bottom by EXACTLY 1.

• When the degree of the top is SMALLER than the degree of the bottom. (x is left over on bottom)

• When the degree of the top is THE SAME as the degree of the bottom. (No x left over)

• When there is a horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

When will a horizontal asymptote NOT exist?

• When the degree of the top is BIGGER than the degree of the bottom.

• When the degree of the top is SMALLER than the degree of the bottom. (x is left over on bottom)

• When the degree of the top is THE SAME as the degree of the bottom. (No x left over)

• When there is a vertical asymptote.

Tags

CCSS.HSF-IF.C.7D

How do you find the zeros?

• Set the simplified denominator equal to zero and solve.

• Set the canceled out parts of the denominator equal to zero and solve.

• Set the simplified numerator equal to zero and solve.

• Use the leading terms only from the top and bottom and simplify.

• Divide the polynomial on the top by the polynomial on the bottom.

Tags

CCSS.HSF-IF.C.7D

How do you find the holes?

• Set the simplified denominator equal to zero and solve.

• Set the canceled out parts of the denominator equal to zero and solve.

• Set the simplified numerator equal to zero and solve.

• Use the leading terms only from the top and bottom and simplify.

• Divide the polynomial on the top by the polynomial on the bottom.

Tags

CCSS.HSF-IF.C.7D

What are the vertical and horizontal asymptotes of

 $\frac{2x+4}{x-2}$  

• vertical: x = 2 horizontal: y = 2

• vertical: x = 2 horizontal: y = -2

• vertical: x = -2 horizontal: y = 2

• vertical: x = -2 horizontal: y = -2

Tags

CCSS.HSF-IF.C.7D

Which could be the graph of

 $\frac{2x+4}{x-2}$  

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Tags

CCSS.HSF-IF.C.7D

Which could be the graph of

 $\frac{x^2-6x-16}{x+5}$  

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Tags

CCSS.HSF-IF.C.7D