Power Functions,Comparing to Exponential and

Log Functions

Lesson 11.6

Compare/Contrast with Exponentials

• Consider

• Try y = x3 and y = 3x

Graph both on your calculator

• Which is larger (or dominates) for low values of x? for very high values of x?

• How many intersections do you find in quadrant 1?

p xy k x y A B

Compare/Contrast with Exponentials

• Note the two functions

Standard ZoomStandard Zoom 0 < x < 50 < y < 50

0 < x < 50 < y < 50

zoom

It is the exponential which eventually will dominate a power

function

It is the exponential which eventually will dominate a power

function

Compare/Contrast with Logarithmic

• Consider

Graph both on your calculator Note differences for small and for

large values of x

1

5 lny x y x

Compare/Contrast with Logarithmic

• Note results of graphing

Standard ZoomStandard Zoom

0 < x < 500 < y < 10

0 < x < 500 < y < 10

Which appearsto dominate?

Which appearsto dominate?

Compare/Contrast with Logarithmic

• The log function appears to dominate But … look at the results of a solve( ) to find

intersections!!

• The exponential eventually dominates!

Long Run Behavior

• Given f(x) = 3x and g(x) = x3

• Complete the following table of values

• Describe the long-run behaviors of f and g as x → -∞ and x →∞

x -3 -2 -1 0 1 2 3

f(x)

g(x)

Assignment

• Lesson 11.6

• Page 472

• Exercises 1 – 37 odd