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EVALUATING FUNCTIONS

EVALUATING 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.

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EVALUATING FUNCTIONS

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  1. EVALUATING FUNCTIONS

  2. 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 r2 --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.

  3. 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) = ___________

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

  5. 3) Let g(x) = x2 + 4 x – 1. Evaluate each of the following: (- 4)2 + 4(- 4) – 1 = 16 – 16 – 1 = - 1 a) g(- 4) = ___________ (8)2 + 4(8) – 1 = 64 + 32 – 1 = 95 b) g(8) = ___________ (- 1)2 + 4(- 1) – 1 = 1 – 4 – 1 = - 4 c) g(- 1) = ___________ (1)2 + 4(1) – 1 = 1 + 4 – 1 = 4 d) g(1) = ___________

  6. 4) Let f(x) = 3x2 – 5 x. Evaluate each of the following: 3(2)2 – 5(2) = 3(4) – 10 = 12 – 10 = 2 a) f(2) = ___________ 3(- 8)2 – 5(- 8) = 3(64) + 40 = 192 + 40 = 232 b) f(- 8) = ___________ c) f(7) = ___________ 3(7)2 – 5(7) = 3(49) – 35 = 147 – 35 = 112 d) f(- 1) = ___________ 3(- 1)2 – 5(- 1) = 3(1) + 5 = 3 + 5 = 8

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

  8. 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

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

  10. 6) Suppose n(x) = 7 x + 4. Determine x such that: x = 0 c) n(x) = 4 ___________ 7 x + 4 = 4 7 x = 0 x = 9/7 = 1.286 d) n(x) = 13 ___________ 7 x + 4 = 13 7 x = 9

  11. 7) Suppose g(x) = - 5 x + 6. Determine x such that: x = - 3 a) g(x) = 21 ___________ - 5 x + 6 = 21 - 5 x = 15 x = 6/5 = 1.2 b) g(x) = 0 ___________ - 5 x + 6 = 0 - 5 x = - 6

  12. 7) Suppose g(x) = - 5 x + 6. Determine x such that: x = 12/5 = 2.4 c) g(x) = - 6 ___________ - 5 x + 6 = - 6 - 5 x = - 12 x = - 8/5 = - 1.6 d) g(x) = 14 ___________ - 5 x + 6 = 14 - 5 x = 8

  13. 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

  14. 8) Suppose g(x) = - 3 x + 8. Determine x such that: x = 22/3 = 7.33 c) g(x) = - 14 ___________ - 3 x + 8 = - 14 - 3 x = - 22 x = - 7/3 = - 2.33 d) g(x) = 15 ___________ - 3 x + 8 = 15 - 3 x = 7

  15. 9) Evaluate the following expressions given the functions below: f(x) = x2 + 7 g(x) = - 3 x + 1 j(x) = 2 x + 9 - 3(10) + 1 = - 30 + 1 = - 29 a) g(10) = ___________ (3)2 + 7 = 9 + 7 =16 b) f(3) = ___________ c) h(- 2) = __________ 2(7) + 9 = 14 + 9 = 23 d) j(7) = __________

  16. 9) Evaluate the following expressions given the functions below: f(x) = x2 + 7 g(x) = - 3 x + 1 j(x) = 2 x + 9 x = - 5 e) Find x if g(x) = 16. ____ - 3 x + 1 = 16 - 3 x = 15 x = - 6 f) Find x if h(x) = - 2. ____ - 2 x = 12 x = 4 g) Find x if f(x) = 23. ____ x2 + 7 = 23 x2 = 16

  17. 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___________

  18. 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

  19. 12) - 3 a.) If f(x) = 7 x – 3, then find f(0). ____ 10 b.) If f(t) = | 5 t |, then find f(2). ____ c.) If g(x) = x2 + 8 x – 6 , then find g(1). ____ 3 d.) If f(b) = 3 b , then find f(3). ____ 9

  20. 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 Find f(200). _____________ 150 f (200) =.75(200) = 150

  21. 14) The profit from selling s number of t-shirts is described by the following function: p(s) = 8 s – 500 Find p(70) __________ 60 p(70) = 8(70) – 500 p(70) = 560 – 500

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

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

  24. 17) Felix’s total credit card balance is described by the following function: c(p) = p(1.30) Find c(2500) __________ 3250 c(2500) = 2500(1.30) c(2500) = 3250

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

  26. 19) The total amount of gas money is determined by the following function: c(g) = Find c($ 3.00) _________ 60

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

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