Graphing Simple Rational Functions

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Presentation transcript:

Graphing Simple Rational Functions

Investigation Graph the following: 1. Y = 3/X 2. Y = 6/X 3. Y = -8/X 4. Y = -4/X What do you notice?!?!?

Rational Function There are 2 basic forms of a rational function 1) 2) Where p(x) & q(x) are polynomials

Rational functions in the form y = are split into parts. Each part is called a BRANCH. To see the direction of your branches look in your calculator and sketch.

Asymptotes An Asymptote is a line (vertical or horizontal) that the graph approaches but NEVER touches!

Asymptotes

What’s domain? The domain of a function is the set of all possible x-values. Vertical Asymptotes are values not included in the domain

What’s range? The range of a function is the set of all possible y-values. Horizontal Asymptotes are values not included in the range

Asymptotes From the form the Vertical Asymptote is when you set x – b = 0 and solve the Horizontal Asymptote is y = c

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 1.

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 2.

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 3.

4. What would an equation of a rational function look like if k=2, it had a H.A. of y = -4, and a V.A. of x = -2 State the Domain and Range Then sketch the graph.