Sketching Rational Functions




                                           all about their
                              ...
http://webct.merlin.mb.ca/
         demo
http://mathway.com/
Factor the polynomial completely. Sketch the graph.
    ƒ(x) = x 3+ 5x 2 + 2x - 8




Step 1:
                            ...
Sketch the graph of
Graphing Rational Functions
 Functions of the form

 where a(x) and b(x) are polynomial functions.

     Examples
Graphing Rational Functions


Appearance


                                      Where n is odd, the
             Where n ...
Graphing Rational Functions

 Sketching (7 steps)


Step 1: Find the y-intercept (let x = 0)


Step 2: Factor everything. ...
Graphing Rational Functions
Step 5: Find the horizontal asymptotes by dividing each term in the
function by the highest po...
Graphing Rational Functions

 Sketching (7 steps)


Step 6: Determine the sign of the function over the intervals defined b...
Graphing Rational Functions

 Sketching: Example 1 of 4

                             Step 5:
 Step 1:


 Step 2:
        ...
Step 5:
Upcoming SlideShare
Loading in...5
×

Pre-Cal 30S January 19, 2009

1,004

Published on

Introduction to graphing rational functions.

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
1,004
On Slideshare
0
From Embeds
0
Number of Embeds
6
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Pre-Cal 30S January 19, 2009

  1. 1. Sketching Rational Functions all about their asymptotic behaviour Capturing the Asymptote by flickr user mindtrip
  2. 2. http://webct.merlin.mb.ca/ demo
  3. 3. http://mathway.com/
  4. 4. Factor the polynomial completely. Sketch the graph. ƒ(x) = x 3+ 5x 2 + 2x - 8 Step 1: Step 4: Step 2: Step 3:
  5. 5. Sketch the graph of
  6. 6. Graphing Rational Functions Functions of the form where a(x) and b(x) are polynomial functions. Examples
  7. 7. Graphing Rational Functions Appearance Where n is odd, the Where n is even, the graph looks like this: graph looks like this:
  8. 8. Graphing Rational Functions Sketching (7 steps) Step 1: Find the y-intercept (let x = 0) Step 2: Factor everything. (Use rational roots theorem if necessary.) Step 3: Find the roots of the function by finding the roots of the numerator a(x). Step 4: Find the vertical asymptotes by finding the roots of the denominator b(x).
  9. 9. Graphing Rational Functions Step 5: Find the horizontal asymptotes by dividing each term in the function by the highest power of x, and take the limit as x goes to infinity. (Use the UNfactored form.) You will find that, in general, there are three possible results: i When [degree of numerator < degree of denominator] the horizontal asymptote is y = 0. ii When [degree of numerator = degree of denominator] the H.A. is the ratio leading coefficient of a(x) leading coefficient of b(x) iii When [degree of numerator > degree of denominator] there is no horizontal asymptote; however there may be a slant asymptote or a hole in the graph.
  10. 10. Graphing Rational Functions Sketching (7 steps) Step 6: Determine the sign of the function over the intervals defined by the roots and vertical asymptotes. (Use the factored form.) Step 7: Sketch the graph.
  11. 11. Graphing Rational Functions Sketching: Example 1 of 4 Step 5: Step 1: Step 2: Step 6: Step 3: Step 7: Step 4:
  12. 12. Step 5:
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×