Power Functions, Comparing to Exponential and Log Functions Lesson 11.6.

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Presentation transcript:

Power Functions, Comparing to Exponential and Log Functions Lesson 11.6

Compare/Contrast with Exponentials Consider Try y = x 3 and y = 3 x  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?

Compare/Contrast with Exponentials Note the two functions Standard Zoom 0 < x < 5 0 < y < 50 zoom 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

Compare/Contrast with Logarithmic Note results of graphing Standard Zoom 0 < x < 50 0 < y < 10 Which appears to 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) = 3 x and g(x) = x 3 Complete the following table of values Describe the long-run behaviors of f and g as x → -∞ and x →∞ x f(x) g(x)

Assignment Lesson 11.6 Page 472 Exercises 1 – 37 odd