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Section 2-5Graphing Special Functions
Vocabulary1. Piecewise-Defined Function:
2. Piecewise-Linear Function:
3. Step Function:
Vocabulary1. Piecewise-Defined Function: A function made up
of two or more expressions
2. Piecewise-Linear Function:
3. Step Function:
Vocabulary1. Piecewise-Defined Function: A function made up
of two or more expressions
2. Piecewise-Linear Function: A function made up of two or more expressions that are all segments or rays
3. Step Function:
Vocabulary1. Piecewise-Defined Function: A function made up
of two or more expressions
2. Piecewise-Linear Function: A function made up of two or more expressions that are all segments or rays
3. Step Function: A function whose graph is a series of horizontal line segments
Vocabulary4. Greatest Integer Function:
5. Absolute Value Function:
Vocabulary4. Greatest Integer Function: A step function where
each non-integer value is rounded down to the nearest integer
5. Absolute Value Function:
Vocabulary4. Greatest Integer Function: A step function where
each non-integer value is rounded down to the nearest integer
5. Absolute Value Function:
f (x) = x! "
Vocabulary4. Greatest Integer Function: A step function where
each non-integer value is rounded down to the nearest integer
5. Absolute Value Function: A function where a V-shaped graph will be created due to applying absolute value to the function
f (x) = x! "
Vocabulary4. Greatest Integer Function: A step function where
each non-integer value is rounded down to the nearest integer
5. Absolute Value Function: A function where a V-shaped graph will be created due to applying absolute value to the function
f (x) = x! "
f (x) = x where f (x) =x if x > 00 if x = 0−x if x < 0
⎧
⎨⎪
⎩⎪
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 1Graph.
f (x) =x −1, if x ≤ 3−1, if x > 3
⎧⎨⎩
x
y
Example 2Write the piecewise-defined function shown in the
graph.
x
f(x)
Example 2Write the piecewise-defined function shown in the
graph.
f (x) =12x − 4, if x < 2
2, if x ≥ 2
⎧⎨⎪
⎩⎪x
f(x)
Example 3Graph.
f (x) = x − 2! "
x
y
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 3Graph.
f (x) = x − 2! "
x
y
x f(x)0 -2
1 -1.5 -2
Example 4Graph.
y = x +1
x
y
Example 4Graph.
y = x +1
x
y
x y
Example 4Graph.
y = x +1
x
y
x y-2
Example 4Graph.
y = x +1
x
y
x y-2 3
Example 4Graph.
y = x +1
x
y
x y-2-1
3
Example 4Graph.
y = x +1
x
y
x y-2-1
32
Example 4Graph.
y = x +1
x
y
x y-2
0-1
32
Example 4Graph.
y = x +1
x
y
x y-2
0-1
321
Example 4Graph.
y = x +1
x
y
x y-2
0-1
1
321
Example 4Graph.
y = x +1
x
y
x y-2
0-1
1
3212
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
3212
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 4Graph.
y = x +1
x
y
x y-2
0-1
12
32123
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation.
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation.
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation.
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
Example 5One psychologist
charges $85 per hour or any fraction thereof for
counseling sessions. Draw a graph that
represents the situation. Cha
rge
($)
85
170
255
340
425
510
Hours1 2 3 4 5 60
