9.3 Graphing Rational Functions Algebra II w/ trig.

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Presentation transcript:

9.3 Graphing Rational Functions Algebra II w/ trig

Remember a rational number is a number that can be written as a fraction. Therefore, a rational function is an equation of the form, where p(x) and q(x) are polynomial expressions and q(x) ≠ 0.

Definitions: - Vertical Asymptotes: a line that the graph approaches but never intersects -To find the vertical asymptotes: set the denominator equal to 0 and solve for x (in other words, your excluded values) - Horizontal Asymptotes: a line that the graph approaches and may intersect - There is at most one horizontal asymptote (y=#) - 3 conditions, based on the equation 1.If n=m, then 2.If n<m, then y=0 3.If n>m, then there is no horizontal asymptote

- X-intercepts: the point(s) in which the graph crosses the x axis -To find the x intercepts, set the numerator equal to 0 and solve. - Y-intercepts: the point(s) in which the graph crosses the y axis -To find the y intercepts, set x equal to 0 in the entire polynomial and solve. - Hole: a point on the graph that does not exist - To find holes factor the numerator and denominator, if any part cancels out, then there is a hole where that part is equal to zero

I. Identify the holes, x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes, then graph by making a table of values. State the domain and range. A.

B.C.

D.E.

F.