M098
Carson Elementary and Intermediate Algebra 3e
Section 8.4
Objectives
1.
2.
3.
Identify the domain and range of a relation and determine if the relation is a function.
Find the value of a function
Graph functions (linear, quadratic, absolute value)
Vocabulary
Relation
Domain
Range
Function
A set of ordered pairs.
The set of all input values for a relation.
The set of all output values for a relation.
A relation in which every value in the domain is paired with exactly one value in the
range.
Prior Knowledge
Finding domain, range and determining if a relation is a function.
Vertical line test to determine if a relation is a function.
Example 1:
{ (-1, 0), (-3, 0), (4, 5), (2, 6) }
Domain: {-1, -3, 4, 2}
Domain is the set of input or x-values.
Range: {0, 5, 6}
Range is the set of output or y-values. Do not repeat a
number if it appears more than once.
Function? Yes
Each x-value is paired to only one y-value. No x-value
repeats. It’s okay if the y-value repeats.
Example 2:
Domain:
[-2, )
{ x | x ≥ -2}
Domain is the set of input or x-values.
Range:
[0, )
Range is the set of output or y-values. Do not repeat a
number if it appears more than once.
{y|y≥0}
Function? Yes
The relation passes the vertical line test.
Evaluating functions
Example 3:
Find f(-3) for f(x) = | x – 4 | +2
f(-3) = | (-3) – 4 | + 2
V. Zabrocki
f(-3) says to substitute -3 for x in the f function and
evaluate it.
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M098
Carson Elementary and Intermediate Algebra 3e
Section 8.4
f(-3) = | -7 | + 2
f(-3) = 9
Graphing linear functions.
We use the slope and the y-intercept to graph a linear function.
Example 4: Graph
f(x) = 3x – 1
y-intercept: (0, -1)
Let x = 0.
slope: 3
The coefficient of the x-term is the slope.
New Concepts
Graph functions.
We can create a table of values to graph other functions as well as quadratic functions.
The basic graphs are often referred to as the library of functions. Here are a couple of other base
functions.
Absolute Value:
Square Root:
f(x) = | x |
f x  
x
-2
-1
0
1
2
Example 5: Graph
y
2
1
0
1
2
x
x
0
1
4
9
16
y
0
1
2
3
4
|x–1|+3
This will be a v-shaped graph. Create a table of values.
Vertex: (1, 3)
V. Zabrocki
x
-2
-1
0
1
2
3
y
6
5
4
3
4
5
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M098
Carson Elementary and Intermediate Algebra 3e
Example 6: Graph
Vertex: (3, 0)
–|x–3|
This will be an upside down, v-shaped graph.
x
-2
-1
0
1
2
3
4
V. Zabrocki
Section 8.4
y
-5
-4
-3
-2
-1
0
-1
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