Objective: Graph rational functions. Identify slant asymptotes.
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Transcript of Objective: Graph rational functions. Identify slant asymptotes.
Objective: Graph rational functions.
Warm up1. Find the following:
a.
b.
c.
d.
2. Find the domain and identify the vertical asymptotes and holes.
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1( )2 3xf x
x x
Vertical Asymptotes: zeros of the denominator. (If there are no common factors for numerator and denominator)
Horizontal Asymptotes: Leading terms
• If n = m;• If m > n; • If m < n; no H.A.
Oblique Asymptotes: when m < n; divide numerator by denominator.
Holes: If there are common factors for numerator and denominators. T At the value of x that makes common factors equal zero.
Example 1Make a table of values to graph . Identify the vertical andand horizontal asymptotes.
Example 2Graph using transformations.
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b.
c.
Example 3Graph
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b.
Assignments:Gizmo: Rational Functions
Carnegie Learning Marathon: 7.1-7.3
Classwork:Pg 355 #37-48
Slant Asymptotes: Degree of numerator is greater. Divide numerator by denominator. ( y = mx+b form).
Example 3Find the slant asymptotes.
a.
b.
Continuation of previous lesson (10/18/12)
Example 5Sketch the graphs. Include asymptotes, intercepts, tables of values used.
a.
b.