Chapter 1: Linear Relations and
Functions
Section 1-7: Piecewise
Functions
Piecewise Functions
z
Different equations are used for different
intervals of the domain. When graphing
piecewise functions, the partial graphs over
various intervals do not necessarily connect.
z
Remember a closed circle means the point is
included and an open circle means the point
is NOT included.
Example #1
⎫
⎧
⎪
⎪2 if x ≤ -5
⎪
⎪
f ( x) = ⎨x + 4 if - 5 < x ≤ 4⎬
⎪
⎪ 1
⎪
⎪- x if x > 4
⎭
⎩ 2
z
Graph
z
Here we have three intervals to look at on the x axis. When x is
less than or equal to -5, y will always be 2 so this part of the graph
is a horizontal line. When x is bigger than -5 but less than or equal
to 4, we have a line with the equation x+4. And when x is bigger
than -4 we have another line with the equation -1/2(x).
The graph is a piecewise function.
z
It is a function because every part satisfies
the vertical line test.
Step Function
z
z
A piecewise function where the graph looks like a set
of stairs is called a step function. In a step function,
there are breaks in the graph of the function.
One type of step function is the greatest integer
function. The symbol x means the greatest integer
not greater than x. For example, 8.9 = 8 because 8 is
the greatest integer not greater than 8.9.
Example #2
z
Graph
f ( x) = 3
x
Absolute Value Function
z
z
The absolute value function is another piecewise
function. The absolute value of a number is always
nonnegative. Notice that the domain includes all real
numbers, but the range includes only nonnegative real
numbers.
Graph f ( x) = − 2 x + 3
HW #6
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z
z
Section 1-7
Pp 49-51
#11,13,14,17,34,36