This preview shows pages 1–5. Sign up to view the full content.
141
L14a
Linear Functions and Models;
Quadratic Functions and Models
Linear Functions
A
linear function
is a function of the form
( )
fx
m
x
b
=
+
Note: The graph of a linear function is a line with the
slope
m
and the
yintercept
b
.
The
domain
of a linear function is the set of all real
numbers.
Example: Graph the function
( )
24
x
=
−+
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 142
Identifying Linear Functions by Using Average Rate of
Change
The
average rate of change
y
x
∆
∆
of a linear function
()
fx
m
x
b
=+
is
constant
and
equal to the slope
m
.
Proof:
Important Note
: A function
( )
is linear if and only if
the average rate of change is constant.
Example
: Find the average rate of change
y
x
∆
∆
of
2
3
9
x
=−
from
1
x
to
2
x
12
x
x
≠
.
143
Example
: A manufacturer has been selling 1000
television sets a week at $450 each.
A market survey
indicates that for each $10 rebate offered to the buyer, the
number of sets sold will increase by 100 per week.
Determine whether the relation between the price
p
and
demand
x
is linear and, if so, express
p
as a linear
function of the demand
x
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 144
Increasing, Decreasing, and Constant Linear Functions
Theorem
: The linear function
( )
fx m
x b
=
+
over its
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/07/2011 for the course MAC 1105 taught by Professor Picklesimer during the Fall '10 term at University of Florida.
 Fall '10
 Picklesimer
 Slope, YIntercept

Click to edit the document details