Rational Functions Review

Operations with Rational Functions

100

Simplify: (5x+15)/(x+3)

What is 5?

200

Multiply: (a² + 7a + 12)/(a² - 9) x (a - 3)/(a+ 3)

What is (a + 4)/(a - 3)

300

Divide: (c² - c - 12)/(c² + 4c + 3) and (c² - 6c + 8)/(c² + 5c + 4)

What is (c + 4)/(c - 2)?

400

Subtract: (x)/(x-4) - (6x)/(x - 5)

What is (-5x² + 19x)/(x - 4)(x - 5)?

500

Simplify: (3x + 6)/(x + 5) / (x + 2)/(x² - 25)

What is 3(x - 5)?

Analyze Graphs of Rational Functions

100

What combination of asymptotes can a rational function have? 

Vertical/Slant OR Vertical/horizontal

200

What is the Horizontal Asymptote of the function: (2x - 3)/(x - 4)?

What is y = 2?

300

Define the hole in the function: (x^2 - 64)/(x^2 + 9x + 8)

What is (-8, 16/7)?

400

What is the Vertical Asymptote of the function: (2x - 3)/(x - 4)?

What is x = 4?

500

Find the slant asymptote 2x²+2x-9/x-1

y=2x+4

Vocabulary

100

What is a rational function?

Any function that is written as a fraction with a variable in the denominator. 

200

When do slant asymptotes occur and how do you find them?

When the degree of the numerator > degree of the denominator, synthetically divide to find the slant? 

300

What is a hole and how do you find it?

An undefined value or gap in your graph; occurs when there is a common factor in the numerator and denominator. 

400

How do you find the Horizontal Asymptote?

When the degree of the of the numerator = degree of denominator, divide the leading coefficients. When the degree of the of the numerator < degree of denominator, y=0. 

500

How do you find vertical asymptotes from an equation?

What makes the denominator equal zero.