Section 3.1 linear functions and their properties

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Section 3.1
Linear Functions and Their
Properties

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( )
2
Graph the linear function: 1
3
f x x= +
−4 −3 −2 −1 1 2 3 4 5
−4
−3
−2
−1
1
2
3
4
x
y
2
This linear function has a slope of and
3
a -intercept of 1 so first plot the point (0,1),
the -intercept.
y
y
2
Next, the slope = so change the
3
-value of the point on the graph by
2 and the -value by 3.
y
x
y
x
∆
∆
2y∆ =
3x∆ =

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Since the average rate of
change is not constant, the
function is not linear.

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Since the average rate of
change is a constant –0.25,
the function is linear.

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IN
C
R
EA
SIN
G
DECR
EASIN
G
CONSTANT

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Determine whether the following linear functions are increasing,
decreasing, or constant.
(a) ( ) 2 4 (b) ( ) 5
3
(c) ( ) (d) ( ) 3
4
f x x g x
s t t m z z
= − + =
= = −
(a) The linear function has a slope of 2 so the function is decreasing.f−
(b) This function could be written g(x) = 0x + 5 so the function has a slope
of 0 and the function g is constant.
3
(c) The linear function has a slope of so the function is increasing.
4
s
(d) The linear function has a slope of 1 so the function is increasing.m