Graphing Rational Functions

 

$\frac{9x^2-25}{x^2+2x+1}$  

Horizontal asymptote?

•  $y=\frac{5}{9}$  

•  $y=-1$  

•  $y=9$  

• None

How do we determine the horizontal asymptote of a rational function?

• Excluded values

• Degrees of the numerator and denominator from the SIMPLIFIED equation

• Set the numerator equal to 0

• Degrees of the numerator and denominator from the ORIGINAL equation

 $g\left(x\right)=\frac{\left(x-2\right)\left(x+7\right)}{\left(x+7\right)\left(x-19\right)\left(x-2\right)}$ 

Direction vertical asymptote?

•  $x=19$  

•  $x=-7$  

•  $x=2$  

• None

• None

When will a rational function have a slant asymptote?

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

• When the degree of the numerator is equal to the degree of the denominator.

• When the degree of the numerator is one greater than the degree of the denominator.

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

 $p\left(x\right)=\frac{x^2-64}{x\left(x-8\right)}$  

x-intercept(s)?

• (0,0)

• (-8,0)

• (8,0)

• (-8,0), (8,0)

Tags

CCSS.HSF-IF.C.7D

• Yes

• No

• Cannot be determined

How do we determine the vertical asymptotes of a rational function?

• Set the simplified denominator equal to 0

• Degrees of the numerator and denominator

• Set the numerator equal to 0

• Set the simplified numerator equal to 0