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

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

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

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

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

More characteristics!!

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.

Determine the domain of these rational functions:

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

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

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

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

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

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