11/21/11 1 11/21/11 2 11/21/11 3 11/21/11 4 11/21/11 Section 9.1
Section 9.2
1.
2.
A biologist notices that the number
of bacteria on her slides increases
by 2 every hour. If there was one
bacterium on her slide 12 hours
ago, how many are on the slide
now?
A biologist notices that a certain
bacterium splits into 2 separate
bacteria once every hour. If there
was one bacterium on the slide 12
hours ago, how many are there on
the slide now?
1. Yes
2.  No
5 11/21/11 





Make a table
Draw a graph
Write an equation
Make a table
Draw a graph
Write an equation
6 11/21/11   Are
functions where dependent variable
changes by a constant factor for every fixed
change in independent variable:
7 11/21/11 1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
All real numbers
Positive real
numbers
Negative real
numbers
Nonnegative real
numbers
Nonpositive real
numbers
All real numbers
Positive real
numbers
Negative real
numbers
Nonnegative real
numbers
Nonpositive real
numbers
8 11/21/11   Domain:
  Range:
  y-intercept
  x-intercept
  asymptote
9 11/21/11 
What if
10 11/21/11 
What if

If f and g are functions for which
◦  f(g(x))=x, for every x in the domain of g
◦  g(f(x))=x, for every x in the domain of f,

Then g is called an inverse function of f and is
usually denoted by f -1
11 11/21/11 1.
2.
Yes
No
1
2
3
4
Domain
5
7
10
12
13
Range
12 11/21/11   What
is the inverse of the function:
f: {(-1,3), (2, 1), (3, 2), (-2,0)}
  The
inverse function switches the roles of
dependent and independent variables:
◦  instead of wanting y in terms of x, we want x in terms of y!
13 11/21/11   How
did you think of this with

The function f gives an expression of y in terms
of x.

To find the inverse of f we need an expression
of x in terms of y:
◦  y=f(x)
◦  Solve for x!
◦  Since we usually consider x the independent, and y
dependent, we exchange y and x.
14 11/21/11   Find
inverse of
  If
(a,b) lies on graph of f, then (b,a) lies on
graph of f -1 .
15