Graphs and Functions
Function Notation

Functions feature some special notation that makes working with them much easier:

The variables x and y are pretty standard in functions and come in handy when you are graphing functions. But mathematicians also use another format called function notation. For example, here are two particular functions named two different ways:

 Traditional expression Function Notation y=3x+2 f(x)=3x+2 y=x2-1 g(x)=x2-1

The symbol f(x) is read as the value of the function at x.

Rudy earns \$25 per hour in his summer job.
a) Write a function f(x) to describe his earnings.
b) Evaluate your function when x=5 hours.
c) How many hours did he work if the earned \$150?
Solution:

a) f(x) = 25x
b) f(5) = 25(5) = \$125
c) 150 = 25x, then x = 6 hours

g(x) = 4x - 3
a) Find g(3)
b) Find x when g(x)=29
Solution:

a) g(3)=4(3)-3=12-3=9
b) 29 = 4x-3 29+3=4x 32=4x x=8

Multiple choice. Which function best models the data:

 x 0 1 2 3 f(x) -1 1 3 5

a) f(x) = -1x+2
b) f(x) = 2x+3
c) f(x) = 2x-1
d) f(x) = 2x
Solution:

f(0) =1, then the function that best models the data is c) f(x) = 2x-1