1. GRAPHING RATIONAL FUNCTIONS ADV122

2. GRAPHING RATIONAL FUNCTIONS ADV122 We have graphed several functions, now we are adding one more to the list! Graphing Rational Functions

3. GRAPHING RATIONAL FUNCTIONS ADV122

4. GRAPHING RATIONAL FUNCTIONS ADV122 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. GRAPHING RATIONAL FUNCTIONS ADV122 Asymptotes Places on the graph the function will approach, but will never touch.

6. GRAPHING RATIONAL FUNCTIONS ADV122 f(x) = 1x1x Vertical Asymptote: x = 0 Horizontal Asymptote: y = 0 Graph: A HYPERBOLA!! No horizontal shift. No vertical shift.

7. GRAPHING RATIONAL FUNCTIONS ADV122

8. GRAPHING RATIONAL FUNCTIONS ADV122 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

9. GRAPHING RATIONAL FUNCTIONS ADV122 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

10. GRAPHING RATIONAL FUNCTIONS ADV122 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

11. GRAPHING RATIONAL FUNCTIONS ADV122

12. GRAPHING RATIONAL FUNCTIONS ADV122 How do we find asymptotes based on an equation only?

13. GRAPHING RATIONAL FUNCTIONS ADV122 Vertical Asymptotes (easy one)

14. GRAPHING RATIONAL FUNCTIONS ADV122 Horizontal Asymptotes (H.A)

15. GRAPHING RATIONAL FUNCTIONS ADV122 3 cases

16. GRAPHING RATIONAL FUNCTIONS ADV122 If the degree of the denominator is GREATER than the numerator. The Asymptote is y=0 ( the x-axis)

17. GRAPHING RATIONAL FUNCTIONS ADV122 If the degree of the denominator and numerator are the same:

18. GRAPHING RATIONAL FUNCTIONS ADV122 If there is a Vertical Shift

19. GRAPHING RATIONAL FUNCTIONS ADV122 Homework http://www.kutasoftware.com/FreeWorksheets /Alg2Worksheets/Graphing%20Simple%20Rati onal%20Functions.pdf http://www.kutasoftware.com/FreeWorksheets /Alg2Worksheets/Graphing%20Simple%20Rati onal%20Functions.pdf http://www.kutasoftware.com/FreeWorksheets /Alg2Worksheets/Graphing%20Simple%20Rati onal%20Functions.pdf http://www.kutasoftware.com/FreeWorksheets /Alg2Worksheets/Graphing%20Simple%20Rati onal%20Functions.pdf