Graphing rational functions

rational

1. INTERVENTION MATERIAL IN GENERAL MATHEMATICS FIRST SEMESTER SY 2016-2017 Prepared by: KRISTEL ANN G. ALDAY Teacher III

2. Warm Up Graph the function  

3. Parent Function:  

4. f(x) = + k a x – h (-a indicates a reflection in the x-axis) vertical translation (-k = down , +k = up ) horizontal translation (+h = left , -h = right ) Pay attention to the transformation clues! Watch the negative sign!! If h = -2 it will appear as x + 2.

5. Vertical Asymptote: x = 0 Horizontal Asymptote: y = 0 f(x) = 1 x Graph: No horizontal shift. No vertical shift. Asymptotes Places on the graph the function will approach, but will never touch.

6. W look like?  

7. Graph: f(x) = 1 x + 4 Vertical Asymptote: x = -4 x + 4 indicates a shift 4 units left Horizontal Asymptote: y = 0 No vertical shift

8. Graph: f(x) = – 3 1 x + 4 x + 4 indicates a shift 4 units left –3 indicates a shift 3 units down which becomes the new horizontal asymptote y = -3. Vertical Asymptote: x = -4 Horizontal Asymptote: y = 0

9. Graph: f(x) = + 6 x x – 1 x – 1 indicates a shift 1 unit right +6 indicates a shift 6 units up moving the horizontal asymptote to y = 6 Vertical Asymptote: x = 1 Horizontal Asymptote: y = 1

10. You try!!  

11. You try!! 2.  

12. How do we find asymptotes based on an equation only?

13. Vertical Asymptotes (easy one) Set the denominator equal to zero and solve for x. Example: x-3=0 x=3 So: 3 is a vertical asymptote.  

14. Horizontal Asymptotes (H.A) In order to have a horizontal asymptote, the degree of the denominator must be the same, or greater than the degree in the numerator. Examples: No H.A because Has a H.A because 3=3. Has a H.A because  

15. 3 cases to consider in determining Horizontal Asymptote of the graph of a Rational Function

16. If the degree of the denominator is GREATER than the numerator. The Asymptote is y=0 ( the x-axis)

17. If the degree of the denominator and numerator are the same: D ivide the leading coefficient of the numerator by the leading coefficient of the denominator in order to find the horizontal asymptote. Example: Asymptote is 6/3 =2.  

18. If there is a Vertical Shift The asymptote will be the same number as the vertical shift. (think about why this is based on the examples we did with graphs) Example: Vertical shift is 7, so H.A is at 7.