Rational Functions

A vertical asymptote is found by setting the _________= to zero and solving for x 

• Numerator
• Denominator
• Right side 
• Left side

Tags

CCSS.HSA.APR.D.7

How do you find the y-intercept?

• replace all x-values with 0

• replace all y-values with 0

• set denominator equal to 0

• compare the degrees of the numerator and denominator

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

How do you find the x-intercept?

• replace all x-values with 0

• replace the y-value with 0 or make the numerator equal 0

• set denominator equal to 0

• compare the degrees of the numerator and denominator

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

How do you determine the Horizontal Asymptote?

• replace all x-values with 0

• replace the y-value with 0 or make the numerator equal 0

• set denominator equal to 0

• compare the degrees of the numerator and denominator

How do you know if a factor in the denominator is a hole instead of a Vertical Asymptote ?

• It cancels out

• it equals 0

• you set the numerator equal to 0

• you compare the degrees

Tags

CCSS.HSA.APR.B.2

When finding the Horizontal Asymptote, if the numerator degree is greater than the denominator degree, the answer is...

• y = 0

• none

• y =a / b

• y=b/a

Tags

CCSS.HSA.APR.D.6

When finding the Horizontal Asymptote, if the numerator degree is equal to the denominator degree, the answer is...

• y = 0

• none

• y =a / b (Leading Coefficient of Numerator/Leading Coefficient of Denominator)

• y= b/a (Leading Coefficient of Denominator/Leading Coefficient of Numerator)

The first thing you should do to find all the attributes for a rational function is...

• Factor it all out

• Find the V.A.

• Find the H.A.

• Find the x / y intercepts

Tags

CCSS.HSA.APR.B.3

Perform the indicated operation:
 $\frac{x^3-9x}{x^2+10x+21}\cdot\frac{x^2+7x}{x^2+5x-24}$  

•  $\frac{2x}{x+8}$  

•  $\frac{x^2}{x+8}$  

•  $\frac{x}{x+4}$  

•  $\frac{x^2\left(x-9\right)}{x+8}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Perform the indicated operation:
 $\frac{x+5}{x^2+18x+80}\div\frac{10x-40}{x^2+6x-40}$  

•  $\frac{10x}{x-6}$  

•  $\frac{x+5}{4x^2}$  

•  $\frac{x+5}{10\left(x+8\right)}$  

•  $\frac{x-1}{6}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3