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.

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

a) g(- 1) = ___________

b) g(- 2) = ___________

c) g(0) = ___________

d) g(5) = ___________

- 5(- 1) + 2 = 5 + 2 = 7- 5(- 2) + 2 = 10 + 2 = 12- 5(0) + 2 = 0 + 2 = 2- 5(5) + 2 = - 25 + 2 = - 23

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

a) f(- 3) = ___________

b) f(6) = ___________

c) f(- 1) = ___________

d) f(4) = ___________

2(- 3) + 2 = - 6 + 2 = - 4

2(6) + 2 = 12 + 2 = 142(- 1) + 2 = - 2 + 2 = 02(4) + 2 = 8 + 2 = 10

3) Let g(x) = x2 + 4 x – 1. Evaluate each of the following:

a) g(- 4) = ___________

b) g(8) = ___________

c) g(- 1) = ___________

d) g(1) = ___________

(- 4)2 + 4(- 4) – 1 = 16 – 16 – 1 = - 1

(8)2 + 4(8) – 1 = 64 + 32 – 1 = 95 (- 1)2 + 4(- 1) – 1 = 1 – 4 – 1 = - 4 (1)2 + 4(1) – 1 = 1 + 4 – 1 = 4

4) Let f(x) = 3x2 – 5 x. Evaluate each of the following:

a) f(2) = ___________

b) f(- 8) = ___________

c) f(7) = ___________

d) f(- 1) = ___________

3(2)2 – 5(2) = 3(4) – 10 = 12 – 10 = 2

3(- 8)2 – 5(- 8) = 3(64) + 40 = 192 + 40 = 232

3(7)2 – 5(7) = 3(49) – 35 = 147 – 35 = 112

3(- 1)2 – 5(- 1) = 3(1) + 5 = 3 + 5 = 8

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

a) f(x) = 18 ___________

b) f(x) = 0 ___________

4 x – 2 = 184 x = 20

x = 5

4 x – 2 = 0

4 x = 2

x = 2/4 = ½ = .5

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

c) f(x) = - 2 ___________

d) f(x) = 12 ___________

4 x – 2 = - 2 4 x = 0

x = 0

4 x – 2 = 12 4 x = 14

x = 14/4 = 7/2 = 3.5

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

a) n(x) = 39 ___________

b) n(x) = 0 ___________

7 x + 4 = 39 7 x = 35

x = 5

7 x + 4 = 0 7 x = - 4

x = - 4/7 = -.571

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

c) n(x) = 4 ___________

d) n(x) = 13 ___________

7 x + 4 = 4 7 x = 0

x = 0

7 x + 4 = 13 7 x = 9

x = 9/7 = 1.286

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

a) g(x) = 21 ___________

b) g(x) = 0 ___________

- 5 x + 6 = 21 - 5 x =

15

x = - 3

- 5 x + 6 = 0

- 5 x = - 6

x = 6/5 = 1.2

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

c) g(x) = - 6 ___________

d) g(x) = 14 ___________

- 5 x + 6 = - 6 - 5 x = - 12

x = 12/5 = 2.4

- 5 x + 6 = 14 - 5 x = 8

x = - 8/5 = - 1.6

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

a) g(x) = 14 ___________

b) g(x) = 0 ___________

- 3 x + 8 = 14 - 3 x = 6

x = - 2

- 3 x + 8 = 0- 3 x = - 8

x = 8/3 = 2.67

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

c) g(x) = - 14 ___________

d) g(x) = 15 ___________

- 3 x + 8 = - 14 - 3 x = - 22

x = 22/3 = 7.33

- 3 x + 8 = 15 - 3 x = 7

x = - 7/3 = - 2.33

9) Evaluate the following expressions given the functions

below:

a) g(10) = ___________b) f(3) = ___________

g(x) = - 3 x + 1

f(x) = x2 + 7j(x) = 2 x

+ 9

xxh

12)(

- 3(10) + 1 = - 30 + 1 = - 29

c) h(- 2) = __________

d) j(7) = __________

(3)2 + 7 = 9 + 7 =16

62

12

2(7) + 9 = 14 + 9 = 23

9) Evaluate the following expressions given the functions

below:g(x) = - 3 x + 1

f(x) = x2 + 7j(x) = 2 x

+ 9

xxh

12)(

e) Find x if g(x) = 16. ____

f) Find x if h(x) = - 2. ____

g) Find x if f(x) = 23. ____

- 3 x + 1 = 16 - 3 x = 15

x = - 5

x

122 - 2 x =

12

x = - 6

x2 + 7 = 23

x2 = 16

x = 4

10) Translate the following statements into coordinate

points:a) f(-1) = 1___________b) h(2) = 7___________c) g(1) = - 1___________d) k(3) = 9___________

(- 1, 1)(2, 7)

(1, - 1)(3, 9)

Given this graph of the function f(x):Find:

11)

a.) f(- 4) = ____b.) f(0) = ____c.) f(3) = ____

d.) f(- 5) = ____e.) x when f(x) = 2

_______f.) x when f(x) = 0

_______

2

0

- 1.75

0

-.9 and 2

0

12)a.) If f(x) = 7 x – 3, then find f(0). ____b.) If f(t) = | 5 t |, then find f(2). ____c.) If g(x) = x2 + 8 x – 6 , then find g(1).

____d.) If f(b) = 3 b , then find f(3). ____

- 3

10

3

9

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). _____________

f (200) =.75(200) = 150

150

14) The profit from selling s number of t-shirts is described by the following function:

p(s) = 8 s – 500

Find p(70) __________

p(70) = 8(70) – 500

p(70) = 560 – 500

60

15) The value of a car is given by the following function:

v(t) = 20,000(.90)t

Find v(1) __________

v(1) = 20,000(.90)(1) v(1) = 18000

18000

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

f(h) = 1,000 + 9 h

Find f(320) __________f(320) = 1000 +

9(320) f(320) = 1000 + 2880

3880

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

c(p) = p(1.30)

Find c(2500) __________c(2500) =

2500(1.30) c(2500) = 3250

3250

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

s(c) = 3 c

Find s(15) __________s(15) = 3(15) = 45

45

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

c(g) =

Find c($ 3.00) _________

30

600g

6030

)3(600)3( c

60

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) _________f(7) = 2(7) = 14

14