1. 26. Graphing Rational Functions
Analyzing and sketching the graph of a rational function

2. Rational Graphing To graph a rational function
Find all the characteristics we learned yesterday (HA, VA, holes, x int, y int)
Put all these on an x-y coordinate plane
Put function into calculator (numerator and denominator must be in ( ) !!! )
Pick an appropriate window to view whole graph
Use calculator as a guide to draw graph on your coordinate plane

3. Example
HA: y=0
VA: x=1
Hole: x=-1
x- int: none
y- int: y=-1

4. Example
HA: y=1
VA: x=1
Hole: x=-1
x- int: none
y- int: y=-1

5. Example
HA: y=0
VA: x=-4,-2
Hole: none
x- int: x=-5
y- int: y=-1

6. More characteristics!!

7. DOMAIN Domain is all the x-values, VA and holes will be excluded.
So it will be found the same as the P of D, just written
in interval form.

8. Determine the domain of these
rational functions:

9. RANGE Range is all the y-values, HA will be excluded.
Sometimes other values are not included,
you must analyze the graph.
We’ll look at these individually when we do examples

10. Rate of Change
Rate of change measures how fast a function is changing – it is the same as slope
2 x-values will be given to you
Plug them into the equation and find the y values (get them from the table in the calculator)
Write these as 2 points
Use the slope formula to calculate the rate of change

11. Find the Rate of Change between x=3 and x=5

12. Graph: HA VA Holes Points of Discontinuity x- intercept y- intercept
Domain
Range
Rate of change between x = 2 and 4

13. Graph: HA VA Holes Points of Discontinuity x- intercept y- intercept
Domain
Range
Rate of change between x = -1 and 1

14. Example HA VA Holes Points of Discontinuity x- intercept y- intercept
Domain
Range
Rate of change between x = 3 and 6