February 17

group work
I've Grown Accustomed to Your Growth
Solutions to I've Grown Accustomed to Your Growth

section covered in text
1.6. Inverse Functions and Logarithms

objective

• to be able to determine if a function has an inverse and how to find that inverse if it does exist
•  to be able to view the logarithmic functions and exponential functions as inverses of each other
• to be able to compare the size of the logarithmic function with any power function

key ideas and/or vocabulary
inverses of algebraic equations, numerical information, graphs of functions and their inverses, and parametric equations; logarithmic functions, properties of logarithms, one-to-one functions, range, domain, cancellation equations of inverse functions

solved problems - using key ideas

• definition of inverse function f ^-1 , its range, domain
• recognizing one-to-one functions, #3,9,13,14
• using the horizontal line test, #5,7,8
• using a graph to determine if a function is one-to-one, #15
• determining  f ^-1 algebraically, #23
• using parametric equations to find inverses (graphing calculator), #53
• using logarithm laws, #35,36,39,40
• determining the value of a logarithm with any base, #41
• determining f ^-1 algebraically using logarithmic and the exponential functions, #26 ,27

announcements
Homework.  #4,8,20,28,50,54
 

QUESTION OF THE DAY

Find the points of intersection of the graphs of the functions  y = 7x and y = x7.

SOLUTION

 

SOLUTION.   There are two points of intersection. The graph below is found in a window [0, 8] x [0, 2x106]. The graph below is found in a window [0,2] x [0, 50].