Graph Simple Rational Functions

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Presentation transcript:

Graph Simple Rational Functions Section 8.2 Graph Simple Rational Functions

California Standard: 7.0: Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions including those with negative exponents in the denominator.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Graph rational functions.

Parent Function for Simple Rational Functions The graph of the parent function is a hyperbola. The domain and range are all nonzero real numbers. Any function of the form ( ) has the same asymptotes, domain, and range as the function Vertical asymptote x=0 Horizontal asymptote y=0

EXAMPLE 1: Graph the function . Compare the graph with the graph of .

Graphing Translations of Simple Rational Functions x=h is the vertical asymptote y=k is the horizontal asymptote Vertical asymptote x=1 x=h Horizontal asymptote y=1 y=k

EXAMPLE 2: Graph the function State the domain and the range.

U-TRY#1: Graph the function. State the domain and range. a) b) c) 8

EXAMPLE 3: Graph the function State the domain and the range.

HOMEWORK Sec 8.2 WS