Graphing Linear Rational Functions

A rational function is a function whose rule is the quotient of two polynomials.

Graphing Linear Rational Functions

Graphing Linear Rational Functions

Graphing Linear Rational Functions

Graphing Linear Rational Functions

Graphing Linear Rational Functions

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Let’s graph …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Let’s graph …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Let’s graph …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Let’s graph …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Let’s graph …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

I like to get a few on either side close to the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

I like to get a few on either side close to the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

I like to get a few on either side close to the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

I like to get a few on either side close to the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Now test a few values to see the rest of the graph…

I like to get a few on either side close to the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Now sketch a smooth curve thru your points getting close to the asymptote lines…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Now sketch a smooth curve thru your points getting close to the asymptote lines…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graph your info …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graph your info …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graph your info …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Graph your info …

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Get some points on either side of the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Get some points on either side of the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Get some points on either side of the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Let’s identify all of our critical information:

Get some points on either side of the vertical asymptote…

Graphing Linear Rational Functions

GENERAL FORMAT FOR LINEAR RATIONAL FUNCTIONS

Now sketch a smooth curve thru your points getting close to the asymptote lines…