Graphing Rational Functions

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Presentation transcript:

Graphing 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 Functions Rational functions in the form y = k/x are split into two parts. Each part is called a BRANCH. If k is POSITIVE the branches are in Quadrants I and III If k is NEGATIVE the branches are in Quadrant II and IV

Asymptotes An asymptote is a line that the graph approaches but NEVER touches!

Find the asymptotes!

Simple Rational Functions the vertical asymptote is x = b the horizontal asymptote is y = c

Identify the asymptotes from the following functions: 1. 2. 3. 4.

Translating Rational Functions Translate Up 3 units and left 2 units 2. Down 5 units and right 1 unit 3. Right 4 units 4. Such that it has a vertical asymptote of x=3 and a horizontal asymptote of y= -2