1. Power Functions, Comparing to Exponential and Log Functions
Lesson 9.6

2. 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?

3. Compare/Contrast with Exponentials
It is the exponential which eventually will dominate a power function
Note the two functions
zoom
Standard Zoom
0 < x < 5 0 < y < 50

4. Compare/Contrast with Logarithmic
Consider
Graph both on your calculator
Note differences for small and for large values of x

5. Compare/Contrast with Logarithmic
Note results of graphing
0 < x < 50 0 < y < 10
Which appears to dominate?
Standard Zoom

6. 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!

7. 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 1 2 3
f(x)
g(x)

8. Assignment
Lesson 9.6
Page 426
Exercises 1 – 37 odd