Linear Function

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Linear Function - PowerPoint PPT Presentation

Linear Function. A Linear Function Is a function of the form where m and b are real numbers and m is the slope and b is the y - intercept . The x – intercept is The domain and range of a linear function are all real numbers. Graph. Graph of a Linear Function.

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PowerPoint Slideshow about ' Linear Function' - emma-blackwell

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Presentation Transcript
Linear Function

A Linear Function Is a function of the form

where mand bare real numbers andm is the slope and bis the

y - intercept. The x – intercept is

The domain and range of a linear function are all real numbers.

Graph

Graph of a Linear Function

The linear function can be graphed using the slope and the y-ntercept

Example If m = 3 b = 2

The linear function can be graphed using the x and the y-intercepts

Average Rate of Change

The average rate of change of a Linear Function is the constant

For example, For f(x)= 5x - 2 , the average rate of change is m =5

Page 121 #15
• f(x) = -3x+4
• The slope is m = -3, the y-intercept b = 4
• The average rate of change is the constant m = -3
• Since m =-3 is negative the graph is slanted downwards. Thus the function is decreasing
Page 121 #19
• f(x) = 3
• f(x)=0x + 3
• m = 0 b = 3
• The average of change is 0
• Since the average rate of change, m = 0
• The function is constant neither increasing or decreasing
Page 121 #21
• To find the zero of f(x), we set f(x) = 0 and solve.
• 2x - 8 = 0
• x = 8/2 = 4
• y-intercept
• Will graph in class
Page 121 #25
• To find the zero of f(x), we set f(x) = 0 and solve.
• x - 8 = 0
• x = 16
• y-intercept
• Will graph in class
Linear or Non Linear Function
• If a function is linear the slope or rate of change is constant
• That is

is always the same

Page 121 #28

The rate of change is not constant. Not a Linear Function

Page 121 #32
• Note the rate of change is constant. It is always
• m =.5 thus the function is linear
Page 121 #38

If g(x) =-2x+30=0

-2x+30=0

-2x = -30, x = 15

y = g(x)

60=-2(-15)+b

b = 30

y =g(x) =-2x +30

If g(x) =-2x+30=20

X = 5

(-15,60)

If g(x) -2x+30=60

-2x+30 60

-2x 30, x 15

(5,20)

(15,0)

If g(x) =-2x+30=60

-2x+30=60

-2x = 30, x = -15

0<2x+30<60

-30 < -2x < 30

15 > x > -15

Page 122 # 44
• Cost Function: C(x) = 0.38x + 5 in dollars
• Find Cost for x = 50 minutes
• C(50) = .38(50) + 5 = 19+5= \$24
• Given Bill, find cost
• C(x) = 0.38x + 5 = 29.32
• 0.38x = 24.32 x = 24.32 /.38 x = 62
• Estimated Cost of Monthly Bill, find Maximum minutes
• 0.38x + 5 = 60 0.38x = 55 x = 55 /.38 x = 144.8
• Can use as many as 144 minutes
Page 122 # 48Supply(S) and Demand(D)
• Equilibrium: Supply = Demand
• S(p) = -2000 + 3000p = D(p) =10,000 -1000p
• -2000 + 3000p =10,000-1000p
• 4000p =12000 p = 3000
• Quantity sold if Demand is less than Supply
• If 10,000 -1000p < -2000 +3000p 4000p > 12000 p > 3000
• The price will decrease if the quantity of demand is less than the quantity of supply
Page 122 # 54Straight Line Depreciation
• Straight Line Depreciation = Book Value / approximate life
• Let V(x) be value of machine after x years
• Cost of machine = Book Value = V(0)
• V(x) = 120,000 – (\$120,000 / 10)x = -12,000x +120,000
Page 122 # 54Straight Line Depreciation(cont)
• Book value after 4years = –12000(4)+1210,000 =120000-8000=72000
• After 4 years the machine will be worth \$72,000