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9.3 Rational Functions and Their Graphs. If the graph is not continuous at x = a then the function has a point of discontinuity at x = a.

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Presentation on theme: "9.3 Rational Functions and Their Graphs. If the graph is not continuous at x = a then the function has a point of discontinuity at x = a."— Presentation transcript:

1 9.3 Rational Functions and Their Graphs

2

3 If the graph is not continuous at x = a then the function has a point of discontinuity at x = a.

4 Ex 1 Find any points of discontinuity.

5 Ex 2 Find any points of discontinuity.

6 Vertical Asymptotes There is a point of discontinuity for each real zero of Q(x). If P(x) and Q(x) have no common real zeros, then the graph has a VA at each real zero of Q(x). If P(x) and Q(x) have a common real zero, a, then there is a hole in the graph or a VA at x = a.

7 Ex 3 Find the VA or holes.

8 Ex 4 Find the VA or holes.

9 Ex 5 Find the VA or holes.

10 Horizontal Asymptotes (There is at most 1 HA per graph.) If the degree of the denominator is > the degree of the numerator then there is a HA at y = 0. If the degree of the numerator is > the degree of the denominator then there is NO HA. If the degree of the numerator = the degree of the denominator then the HA is y = a/b where a is the leading coefficient of the numerator & b is the LC of the denominator.

11 Ex 6 Find the VA, HA, and holes.

12 Ex 7 Sketch the graph and identify the VA, HA, and holes.

13 The zero of the numerator is the x- intercept!!


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