Linear function
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Linear Function PowerPoint PPT Presentation


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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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Linear Function

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Linear function

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

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

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

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

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

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

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

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

Page 121 #28

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


Page 121 32

Page 121 #32

  • Note the rate of change is constant. It is always

  • m =.5 thus the function is linear


Page 121 38

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

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 48 supply s and demand d

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 =12000p = 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 54 straight line depreciation

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 54 straight line depreciation cont

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


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