Rational Functions Test Review

Vertical Asymptotes and Holes

100

How do you find the Vertical Asymptote of a Rational Function? 

Set the Denominator equal to zero! Check with your calculator! 

200

How can we tell if there is a Hole in the graph for a Rational Function? 

1. Factor both the Numerator and the Denominator

2. Are matching factors present on both the top and the bottom? 

3. If yes, set the factors equal to zero and solve! 

300

Find the Vertical Asymptote, Hole, Horizontal Asymptote and X-Intercepts of the Rational Function: 

f(x) = (x-2) / (x-4) 

VA: x=4

Hole: None

HA: y=1

X- intercept: (2,0)

400

Find the Vertical Asymptote, Hole, Horizontal Asymptote and X-Intercepts of the Rational Function: 

f(x) = (x²+x-6) / (-4x²-16x-12) 

VA: x= -1

Hole: x= -3

HA: y= -1/4

X-intercept: (2,0)

500

Find the Vertical Asymptote, Hole and Horizontal Asymptote of the Rational Function: 

f(x) = (x-4) / (-4x-16) 

VA: x= -4

Hole: None

HA: y= -1/4

Horizontal and Slant Asymptotes

100

Can you have both a Horizontal and a Slant Asymptote? 

NO

200

What does BOT = NO mean? 

This is for Horizontal Asymptotes! 

If the highest degree of the polynomial on the Numerator is BIGGER than the highest degree of the polynomial on the Denominator...there is NO HORIZONTAL ASYMPTOTE

300

Find the Horizontal or Slant Asymptote of the Rational Function:

(x²-6x+7) / (x+5)

The degree of the numerator is greater than the denominator so we have a Slant Asymptote. 

SA: x-11

400

Find the Horizontal Asymptote: 

(x+3) / (x²+9) 

HA: Y= 0

*BOB = 0

500

Find the Slant Asymptote: 

(5x³-8) / (x²+3x-1) 

SA: 5x- 15

*Don't forget your place holders when dividing! 

Solving Rational Equations

100

What is the first step when solving Rational Equations? 

Factor the numerator and denominator (if needed)! Then find your LEAST COMMON DENOMINATOR!

Remember to solve for extraneous solutions! 

200

Why MUST you check your answers when solving Rational Equations? 

There can be Extraneous Solutions! 

300

Solve: 

2/(x+4) + 7/(x-1) = (x-6)/(x²+3x-4) 

No solution

400

Solve: 

5/(x+3) + 2/(x-3) = 5/(x²-9)

x= 2

500

Solve: 

32/(x²-16) + 5 = x/(x+4) 

x=3

Bonus!

100

How do you find the Horizontal Asymptote of a Rational Function if the degree of the numerator is the same as that of the denominator? 

Look at the leading coefficients! Numerator over denominator!

*BOS = CO 

200

Where do you find the y-intercept in the equation for a Rational Function? 

Look at the constants of the numerator and denominator before you factor! 

300

What is the best kind of cookie? 

Chocolate Chip

400

How can you find the x-intercepts for a Rational Function? 

1.) You can always graph it :)

2.) Factor the numerator and look at the values that give you zero! (beware of Holes)

500

Solve: 

(x³-x²-6x) / (-3x²-3x+18) 

VA:x= -3, 2

Hole: None

HA: None

X-intercept: (0,0) (-2,0) (3,0)