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**3 hr 5 hr 8 hr Hours worked Charge**

A plumber charged $110 for a three hour job and $160 for a five hour job. At this rate, how much would he charge for an eight hour job. plumbers normally charge a basic fee to just show up, and then they charge per hr. Hours worked Charge 3 hr $110 5 hr $160 8 hr $?

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240 $235 220 200 180 160 140 120 100 80 Distance 60 40 20 1 2 3 4 5 6 7 8 9 10 11 12 Time

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**Lesson 3.8 Linear Functions f(2) = 5 ( 2, 5) Function notation**

A linear function is a linear equation written with f(x) instead of y Function notation Equation notation Input, output Ordered Pair f(2) = 5 ( 2, 5)

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**f(x) = x + 4 Example: Find an equation of the linear function f**

a) m = , b = 4 f(x) = mx + b f(x) = x + 4

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f(-2) = 1 , m = 3 b) step1: Rewrite the function notation as ordered pair x1 y1 f(-2) = 1 (-2, 1) step2: write the equation using the point slope form y – y1 = m(x – x1) y – 1 = 3(x + 2) y – 1 = 3x + 6 y = 3x + 7 step3: write the equation in the function notation. f(x) = 3x + 7

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f(0) = 7 , f(4) = -1 c) step1: rewrite the function notation as ordered pair f(0) = 7 f(4) = -1 (0, 7) (4, -1) x1 y1 x2 y2 step2: find the slope (0, 7) and (4, -1) step3: write the equation using the point slope form y – y1 = m(x – x1) y – 7 = -2(x – 0) y – 7 = -2x y = -2x + 7 step4: write the equation in the function notation. f(x) = -2x + 7

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**f is a linear function f(x) = -x + 4 d) **

If f(1) = 3 , f(-1) = 5, find f(10)=? and f(100)=? step1: rewrite the function notation as ordered pair f(1) = 3 (1, 3) f(-1) = 5 (-1, 5) x1 y1 x2 y2 step2: find the slope (1, 3) and (-1, 5) step3: write the equation using the point slope form step5: find f(10) and f(100) y – y1 = m(x – x1) f(10) = - (10) + 4 y – 3 = -1(x – 1) = -6 y – 3 = -x + 1 y = -x + 4 f(100) = -(100) + 4 step4: write the equation in the function notation. = -96 f(x) = -x + 4

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Home Work (2 – 22 + even 28, 29, 30) Page 149, 150

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Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = 10 11 x 1 = 11 12 x 1 = 12 X 2 1.

Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = 10 11 x 1 = 11 12 x 1 = 12 X 2 1.

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