Download presentation

Presentation is loading. Please wait.

Published byCedric Bollen Modified over 2 years ago

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

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google