section 3.1 linear functions and their properties
TRANSCRIPT
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Section 3.1
Linear Functions and Their Properties
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2Graph the linear function: 1
3f x x
x
y2
This linear function has a slope of and3
a -intercept of 1 so first plot the point (0,1),
the -intercept.
y
y
2Next, the slope = so change the
3-value of the point on the graph by
2 and the -value by 3.
y
xy
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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INCREASING
DECREASING
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
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Let ( ) represent the value of each car after years.V x x
(0) $28,000 and the slope is 4000 since the car depreciates
by that amount per year.
V
( ) 4000 28000V x x
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3 4000 3 28,000 16,000V
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(d) The slope is the average rate of change and is –4000 so this means that for each additional year that passes, the book value of the car decreases by $4000.
(e) 8000 4000 28000x
20000 4000x 20000
54000
x
The car will have a book value of $8000 when it is 5 years old.
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60 900 15 2850p p 75 3750p 50p
50 60 50 900 2100s
So the equilibrium price is $50 and the equilibrium quantity is 2100 phones.
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60 900 15 2850p p
75 3750p
50p
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