WRITING EQUATIONS OF RATIONAL FUNCTIONS

Advanced AlgebraDr. ShildneckSpring, 2015

CHARACTERISTICS OF RATIONAL FUNCTIONS

Things to Remember: Vertical Asymptotes come from the

denominator

Horizontal Asymptotes result from smaller or equal degrees in numerator

Slant Asymptotes result from dividing a 1-degree bigger numerator by the denominator

CHARACTERISTICS OF RATIONAL FUNCTIONS

Things to Remember: Y-Intercepts occur when x = 0.

X-Intercepts (zeros) occur when y = 0.

A General point occurs when x is plugged in to get a y-value.

Holes occur whenever there is a common factor between the numerator and denominator.

CHARACTERISTICS OF RATIONAL FUNCTIONS

Things to Remember: Whenever you are given a specific x-value,

it’s related factor is (x – that number).

For example, given x = 5, It’s factor is (x-5)

And given x = -5, It’s factor is (x+5)

WRITING THE EQUATIONS – IN GENERAL Determine the vertical asymptotes (VA)

Write a factor for each in the denominator

Determine the horizontal asymptotes (HA) Determine a factor that would result in that HA based

on the rules for asymptotes

If there is a slant asymptote (SA), “un-divide” the numerator and denominator In other words, multiply. But! Then, add 1 to the answer.

WRITING EQUATIONS – SPECIFIC CASES If there are holes, multiply in a factor in

both the numerator and denominator.

If you are given a point (x, y): make the constant part of the numerator a

variable, like (x-b) or (x-h). Plug in the x-value for x and set equal to

the y-value Solve for your variable constant

FINAL ANSWERS

Your final answer should be written as a function of x It should start with “y =“ or “f(x)=“ It should have x variables and numbers. No

other letters.

You may leave it in factored form. Do not multiply out the factors.

EXAMPLE 1

Write an equation of a rational function with the following characteristics.

VA: x = -7HA: y = 0

EXAMPLE 2

Write an equation of a rational function with the following characteristics.

VA: x = 12HA: y = 3

EXAMPLE 3

Write an equation of a rational function with the following characteristics.

VA: x = -3HA: y = 1Y-int: (0, 5)

EXAMPLE 4

Write an equation of a rational function with the following characteristics.

VA: x = -1HA: y = 2Hole at: x = 5

EXAMPLE 5

Write an equation of a rational function with the following characteristics.

VA: x = -1, x = 1SA: y = 2x-3

ASSIGNMENT

Worksheet Number 7Writing Equations of Rational

Functions