Precalculus:
1.1 IN-CLASS
Function Notation and Evaluating Piecewise Functions
Function Notation
As you have seen, functions can be written as a mapping, as ordered pairs, as equations, and
drawn as graphs. All of these are interrelated. A mapping can be changed to a list of ordered
pairs. Ordered pairs can be graphed. The points on the graphs can be listed as a set of ordered
pairs. Sometimes we can write the equations of the graphs.
There is also a relationship between the function notation we use and ordered pairs. It is
f(a) = b ↔ (a, b)
Thus, we can go back and forth between the two notations.
Examples
I. Change the following from function notation to ordered pairs.
a. f(3) = 7
b. f(-4) = 9
c. g(8) = -20
II. Change the following from ordered pairs into function notation.
a. (12, 5)
b. (-7, -10)
c. (-3, 4)
III. Write the equations of the following functions using function notation.
a.
b.
________________________
_______________________
Evaluating Piecewise Functions
Recall the definition of a function: A relation for which there is exactly one output for each
input. A piecewise function is a function that has different pieces to it. A graph of a piecewise
function might look like this:
When written as an equation, piecewise functions will be written in parts. However, since it is a
function, for every x that you put into it, you can only get out one value of y, so you have to
choose which part of the function it goes into so that you get only one answer out.
Examples
 2x 1 x  3

f ( x)   1
x4 x 3

2
x  1
 2x

g ( x)  3x  2 1  x  4
 5
x4

 x4

h( x )   3
2
5 x  3

x5
x5
I. Evaluate the following using the functions above.
a. f(1)
b. f(6)
c. g(-5)
d. g(8)
e. g(0)
f. h(-3)
g. h(3)
h. h(5)
II. Evaluate the following using the functions above. Write your answers as ordered pairs.
a. f(-12)
b. h(8)
c. g(-1)
d. g(4)