Graphing Rational Expressions

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Presentation transcript:

Graphing Rational Expressions

Find the domain: Graph it:

Find the domain: Graph it:

Vertical Asymptote If (x – a) is a factor of the denominator of a rational function but not a factor of the numerator, then x = a is a vertical asymptote of the graph of the function.

Find the domain: Graph it using the graphing calculator:

Hole (in the graph) If (x – b) is a factor of both the numerator and denominator of a rational function, then there is a hole in the graph of the function where x = b, unless x = b is a vertical asymptote. The exact point of the hole can be found by plugging b into the function after it has been simplified.

Find the domain and identify vertical asymptotes & holes.

Find the domain and identify vertical asymptotes & holes.

Find the domain and identify vertical asymptotes & holes.

Find the domain and identify vertical asymptotes & holes.

Horizontal Asymptotes Degree of numerator = Degree of denominator Degree of numerator < Degree of denominator Degree of numerator > Degree of denominator Horizontal Asymptote: Horizontal Asymptote: Horizontal Asymptote:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph:

Find all asymptotes & holes & then graph: