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Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 1) Factor the numerator and the denominator 2) State the domain.

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Presentation on theme: "Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 1) Factor the numerator and the denominator 2) State the domain."— Presentation transcript:

1 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 1) Factor the numerator and the denominator 2) State the domain and the location of any holes in the graph 3) Simplify the function to lowest terms 4) Find the y-intercept (x = 0) and the x-intercept(s) (y = 0) 5) Identify any existing asymptotes (vertical, horizontal, or oblique

2 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 8) Analyze the behavior of the graph on each side of an asymptote 9) Sketch the graph 6) Identify any points intersecting a horizontal or oblique asymptote. 7) Use test points between the zeros and vertical asymptotes to locate the graph above or below the x-axis

3 Section 5.3 – The Graph of a Rational Function Example 1) Factor the numerator and the denominator 2) State the domain and the location of any holes in the graph 3) Simplify the function to lowest terms No holes

4 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 4) Find the y-intercept (x = 0) and the x-intercept(s) (y = 0) y-intercept (x = 0) x-intercept(s) (y = 0) Use numerator factors

5 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 5) Identify any existing asymptotes (vertical, horizontal, or oblique Horiz. Or Oblique AsymptotesVertical Asymptotes Use denominator factors Examine the largest exponents

6 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 6) Identify any points intersecting a horizontal or oblique asymptote.

7 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 7) Use test points between the zeros and vertical asymptotes to locate the graph above or below the x-axis

8 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 7) Use test points between the zeros and vertical asymptotes to locate the graph above or below the x-axis

9 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function ) Analyze the behavior of the graph on each side of an asymptote

10 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 8) Analyze the behavior of the graph on each side of an asymptote

11 Section 5.3 – The Graph of a Rational Function 9) Sketch the graph

12 Section 5.3 – The Graph of a Rational Function Example 1) Factor the numerator and the denominator 2) State the domain and the location of any holes in the graph 3) Simplify the function to lowest terms

13 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 4) Find the y-intercept (x = 0) and the x-intercept(s) (y = 0) y-intercept (x = 0) x-intercept(s) (y = 0) Use numerator factors

14 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 5) Identify any existing asymptotes (vertical, horizontal, or oblique Horiz. Or Oblique AsymptotesVertical Asymptotes Use denominator factors Examine the largest exponents

15 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 6) Identify any points intersecting a horizontal or oblique asymptote.

16 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 7) Use test points between the zeros and vertical asymptotes to locate the graph above or below the x-axis -3 2

17 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 8) Analyze the behavior of the graph on each side of an asymptote -3 2

18 Section 5.3 – The Graph of a Rational Function 9) Sketch the graph

19 Section 5.3 – The Graph of a Rational Function Example 1) Factor the numerator and the denominator 2) State the domain and the location of any holes in the graph 3) Simplify the function to lowest terms No holes

20 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 4) Find the y-intercept (x = 0) and the x-intercept(s) (y = 0) y-intercept (x = 0) x-intercept(s) (y = 0) Use numerator factors

21 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 5) Identify any existing asymptotes (vertical, horizontal, or oblique Horiz. or Oblique Asymptotes Vertical Asymptotes Use denominator factors Examine the largest exponents Oblique: Use long division

22 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 6) Identify any points intersecting a horizontal or oblique asymptote.

23 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 7) Use test points between the zeros and vertical asymptotes to locate the graph above or below the x-axis -2 1

24 Section 5.3 – The Graph of a Rational Function General Steps to Graph a Rational Function 8) Analyze the behavior of the graph on each side of an asymptote 1

25 Section 5.3 – The Graph of a Rational Function 9) Sketch the graph


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