REAL WORLD EXAMPLES OF f x The real

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REAL WORLD EXAMPLES OF f (x) The real world—round, fast-paced, expensive— relies on functions!

REAL WORLD EXAMPLES OF f (x) The real world—round, fast-paced, expensive— relies on functions! --The circumference of a circle, C(r), depends on its radius, r. C(r) = 2 п r --The area of a circle, A(r), depends on its radius, r. A(r) = п r 2 --The distance, D(r), from home to work depends on the time, t, spent driving at an average speed of r miles an hour. D(r) = r t --The value, V(t), of an investment, P, with an annual return of r %, depends on t years. V(t) = P r t.

1) Let g(x) = - 5 x + 2. Evaluate each of the following:

1) Let g(x) = - 5 x + 2. Evaluate each of the following: - 5(- 1) + 2 = 5 + 2 = 7 a) g(- 1) = ______ 5(- 2) + 2 = 10 + 2 = 12 b) g(- 2) = -______ - 5(0) + 2 = 0 + 2 = 2 c) g(0) = ______ - 5(5) + 2 = - 25 + 2 = - 23 d) g(5) = ______

2) Let f(x) = 2 x + 2. Evaluate each of the following: 3)

2) Let f(x) = 2 x + 2. Evaluate each of the following: 3) + 2 = - 6 + 2 = - 4 a) f(- 3) = 2(______ + 2 = 12 + 2 = 14 b) f(6) = 2(6) ______ 1) + 2 = - 2 + 2 = 0 c) f(- 1) = 2(______ 2(4) + 2 = 8 + 2 = 10 d) f(4) = ______

4) Let f(x) = 3 x 2 – 5 x. Evaluate each of the

4) Let f(x) = 3 x 2 – 5 x. Evaluate each of the following: 2 – 5(2) = 3(4) – 10 = 12 – 10 = 2 3(2) a) f(2) = ______ 3(- 8)2 – 5(- 8) = 3(64) + 40 = 192 + 40 = 232 b) f(- 8) = ______ 2 – 5(7) = 3(49) – 35 = 147 – 35 = 112 c) f(7) = 3(7) ______ 1)2 – 5(- 1) = 3(1) + 5 = 3 + 5 = 8 d) f(- 1) = 3(______

5) Suppose f(x) = 4 x – 2. Determine x such that: x =5

5) Suppose f(x) = 4 x – 2. Determine x such that: x =5 a) f(x) = 18 ______ 4 x – 2 = 18 4 x = 20 2/ = ½ =. 5 x = b) f(x) = 0 ______ 4 4 x– 2=0 4 x=2

5) Suppose f(x) = 4 x – 2. Determine x such that: c) f(x)

5) Suppose f(x) = 4 x – 2. Determine x such that: c) f(x) = - 2 ______ x=0 4 x– 2=-2 4 x=0 x = 14/4 = 7/2 = 3. 5 d) f(x) = 12 ______ 4 x – 2 = 12 4 x = 14

6) Suppose n(x) = 7 x + 4. Determine x such that: x=5 a)

6) Suppose n(x) = 7 x + 4. Determine x such that: x=5 a) n(x) = 39 ______ 7 x + 4 = 39 7 x = 35 4/ = -. 571 x = b) n(x) = 0 ______ 7 7 x+4=0 7 x=-4

6) Suppose n(x) = 7 x + 4. Determine x such that: x =0

6) Suppose n(x) = 7 x + 4. Determine x such that: x =0 c) n(x) = 4 ______ 7 x+4=4 7 x =0 9/ = 1. 286 x = d) n(x) = 13 ______ 7 7 x + 4 = 13 7 x=9

7) Suppose g(x) = - 5 x + 6. Determine x such that: x

7) Suppose g(x) = - 5 x + 6. Determine x such that: x =-3 a) g(x) = 21 ______ - 5 x + 6 = 21 - 5 x = 15 6/ = 1. 2 x = 5 b) g(x) = 0 ______ -5 x+6=0 -5 x=-6

7) Suppose g(x) = - 5 x + 6. Determine x such that: 12/

7) Suppose g(x) = - 5 x + 6. Determine x such that: 12/ = 2. 4 x = 5 c) g(x) = - 6 ______ -5 x+6=-6 - 5 x = - 12 8/ = - 1. 6 x = 5 d) g(x) = 14 ______ - 5 x + 6 = 14 -5 x=8

8) Suppose g(x) = - 3 x + 8. Determine x such that: x

8) Suppose g(x) = - 3 x + 8. Determine x such that: x =-2 a) g(x) = 14 ______ - 3 x + 8 = 14 -3 x =6 x = 8/3 = 2. 67 b) g(x) = 0 ______ -3 x+8=0 -3 x=-8

8) Suppose g(x) = - 3 x + 8. Determine x such that: 22/

8) Suppose g(x) = - 3 x + 8. Determine x such that: 22/ = 7. 33 x = c) g(x) = - 14 ______ 3 - 3 x + 8 = - 14 - 3 x = - 22 7/ = - 2. 33 x = 3 d) g(x) = 15 ______ - 3 x + 8 = 15 -3 x=7

9) Evaluate the following expressions given the functions below: g(x) = - 3 x

9) Evaluate the following expressions given the functions below: g(x) = - 3 x + 1 f(x) = x 2 + 7 j(x) = 2 x + 9 - 3(10) + 1 = - 30 + 1 = - 29 a) g(10) = ______ 2 + 7 = 9 + 7 =16 (3) b) f(3) = ______ c) h(- 2) = _____ d) j(7) = 2(7) + 9 = 14 + 9 = 23

9) Evaluate the following expressions given the functions below: g(x) = - 3 x

9) Evaluate the following expressions given the functions below: g(x) = - 3 x + 1 f(x) = x 2 + 7 j(x) = 2 x + 9 =-5 e) Find x if g(x) = 16. x____ - 3 x + 1 = 16 - 3 x = 15 =-6 f) Find x if h(x) = - 2. x____ - 2 x = 12 =4 g) Find x if f(x) = 23. x____ x 2 + 7 = 23 x 2 = 16

10) Translate the following statements into coordinate points: (- 1, 1) a) f(-1) =

10) Translate the following statements into coordinate points: (- 1, 1) a) f(-1) = 1______ (2, 7) b) h(2) = 7______ (1, - 1) c) g(1) = - 1______ (3, 9) d) k(3) = 9______

11) Given this graph of the function f(x): Find: 2 a. ) f(- 4)

11) Given this graph of the function f(x): Find: 2 a. ) f(- 4) = ____ 0 b. ) f(0) = ____ - 1. 75 c. ) f(3) = ____ 0 d. ) f(- 5) = ____ e. ) x when f(x) = 2 -. 9 and 2 _______ f. ) x when f(x) = 0 0 _______

12) a. ) If f(x) = 7 x – 3, then find f(0). ____

12) a. ) If f(x) = 7 x – 3, then find f(0). ____ -3 10 b. ) If f(t) = | 5 t |, then find f(2). ____ c. ) If g(x) = x 2 + 8 x – 6 , then find g(1). ____ 3 d. ) If f(b) = 3 b , then find f(3). 9 ____

13) Denise decides to study abroad in France. She has to exchange her dollars

13) Denise decides to study abroad in France. She has to exchange her dollars for Euros. The following function describes the exchange rate between dollars and Euros: f(d) =. 75 d 150 Find f(200). _______ f (200) =. 75(200) = 150

14) The profit from selling s number of tshirts is described by the following

14) The profit from selling s number of tshirts is described by the following function: p(s) = 8 s – 500 60 Find p(70) _____ p(70) = 8(70) – 500 p(70) = 560 – 500

15) The value of a car is given by the following function: v(t) =

15) The value of a car is given by the following function: v(t) = 20, 000(. 90)t 18000 Find v(1) _____ v(1) = 20, 000(. 90)(1) v(1) = 18000

16) Daniel’s income for the fall semester is described by the following function: f(h)

16) Daniel’s income for the fall semester is described by the following function: f(h) = 1, 000 + 9 h 3880 Find f(320) _____ f(320) = 1000 + 9(320) f(320) = 1000 + 2880

17) Felix’s total credit card balance is described by the following function: c(p) =

17) Felix’s total credit card balance is described by the following function: c(p) = p(1. 30) 3250 Find c(2500) _____ c(2500) = 2500(1. 30) c(2500) = 3250

18) The study time per credit hour is described by the following function: s(c)

18) The study time per credit hour is described by the following function: s(c) = 3 c 45 Find s(15) _____ s(15) = 3(15) = 45

19) The total amount of gas money is determined by the following function: c(g)

19) The total amount of gas money is determined by the following function: c(g) = 60 Find c($ 3. 00) _____

20) The number of Facebook friends you make d days after arriving on campus

20) The number of Facebook friends you make d days after arriving on campus is described by the following function: f(d) = 2 d 14 Find f(7) _____ f(7) = 2(7) = 14

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