Functions Are Usually Named by Letters (Upper Or Lower Case)

Lesson 11, Section 2.2 (Part 2)

I Function Notation

Functions are usually named by letters (upper or lower case).

f (x) is called function notation, read 'f of x' and represents the function f with domain x. It means the same thing as y. *Note: f(x) does not mean f times x!!!

x  rule of correspondence  y or f (x)

1. f :{(3,2),(1,3),((2,2)} f (3) 

a) Find: f (1)  f (2) 

f (x)  2

b) Find the value of x such that... f (x)  3 f (x)  2

2. f (3,4) (2,3)

(-5, -3)

(0,-3)

(-8, -6)

f (8) 

a) Find f (2)  f (3)  f (x)  3 b) Find the value of x such that... f (x)  3 f (x)  6

*Note: f(x) does not mean f times x!!!

  1   3. g: (0,2), ,3),(3,1),(1,2)   2   g(3) a) Find: g(- 1) g(0)

g( x )= 3 b) Find the value of x such that.... g( x )= 2

h(2)  a) Find: h(0) 

h( x )= 0 b) Find x such that.... h( x )= - 2 3 5. r(t)  t  4 2

r(2) 

a) Find f (2)  r(8) 

f( t )= 8 b) Find t such that f( t )= 2 f( t )= - 2

6) a) Find g (3) for g(x)  2x 1

b) Find f (-1) for f (t)  5t 2  t

c) Find h (4) for h (x) = 2

d) Find f (a) for f (x)  6x 1

e) Find g(a 1) for g(x)  2x  3

f) Find h(3m) for h(x)  5x 2  4x

x  2 g) Find f (0) for f (x)  2x  3 x  2 h) Find f (x  2) for f (x)  2x  3

Function Models

A Surface area of a sphere is given by A(r)  4 r 2

Find the surface area of the sphere when radius is 5 cm. Give an exact value and an approximation using 3.14 for pi.

5 B Celsius temperature is given by C(F)  (F  32) . 9

a) Find Celsius temperature if Fahrenheit temperature is 50 degrees.

b) Find Celsius temperature if Fahrenheit temperature is -4 degrees. The following graph ( f( t ) )shows the percentage of people who responded 'yes' to the question, 'If your party nominated a well-qualified woman candidate for president, would you vote for that person?'

t a) Use the graph to approximate the percentage of people who said 'yes' for 1960? 1980?

b) If the trend continues, how many would you approximate would say 'yes' for 2008? B Compact fluorescent lightbulbs (CFL) can be used to most places that conventional incandescent bulbs are, but use a fraction of the electricity. This table lists the CFL wattage and the incandescent wattage required to create the same amount of light. CFL wattage Incandescent equivalent 7 25 20 75 30 120

Use the data to draw a graph and estimate the wattage of an incandescent bulb that reates light equivalent to a 15-watt CFL bulb? 35-watt CFL bulb?

150 t n e l a v i u q e t n e c s 100 e d n a c n I

10 f(x)

5 10 15 20 25 30 35 40

x CFL Wattage