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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

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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

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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

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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

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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

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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

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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

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Linear or Non Linear Function If a function is linear the slope or rate of change is constant That is is always the same

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Page 121 #28 XY=f(x) -2¼ ½ 01 12 24 The rate of change is not constant. Not a Linear Function

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Page 121 #32 xy = f(x) -2-4 -3.5 0-3 1-2.5 2-2 Note the rate of change is constant. It is always m =.5 thus the function is linear

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Page 121 #38 (15,0) (5,20) (-15,60) y = g(x) 60=-2(-15)+b b = 30 y =g(x) =-2x +30 If g(x) =-2x+30=20 X = 5 If g(x) =-2x+30=60 -2x+30=60 -2x = 30, x = -15 If g(x) =-2x+30=0 -2x+30=0 -2x = -30, x = 15 If g(x) -2x+30=60 -2x+30 60 -2x 30, x 15 0<2x+30<60 -30 < -2x < 30 15 > x > -15

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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

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Page 122 # 48 Supply(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 12000 p > 3000 The price will decrease if the quantity of demand is less than the quantity of supply

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Page 122 # 54 Straight 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

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Page 122 # 54 Straight 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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