Page 162 - Algebra 1

Example
2
Identifying a Set of Ordered Pairs as a Function
a. Determine whether {(3, 3), (10, 1), (0, 3), (8, 9), (4, 4), (10, 2)} represents a function.
Hint
When you write the domain and range, only write 10 and 3 once.
Domain: {0, 3, 4, 8, 10} Range: {1, 2, 3, 4, 9}
SOLUTION
Each domain value must map with exactly one range value.
The diagram shows that the domain value of 10 maps to the range values 1 and 2.
The relation is not a function. Each domain value does not have exactly one range value.
3 1 10 3 0 9 8 4 4 2
b. Determine whether y = _1 x - 1 represents a function. 2
SOLUTION
No matter what value is substituted for the independent variable x, the equation outputs exactly one value for the dependent variable y.
The equation represents a function.
If a relation is graphed on a coordinate grid, the vertical-line test can be used to determine if the relation is a function.
Domain (x)
-6
0
2
5
7
10
Range (y)
-4
-1
0
_3 2
_5 2
4
Vertical-Line Test
A graph on the coordinate plane represents a function if any vertical line intersects the graph in exactly one point.
y
x
The relation is not a function. The vertical-line cuts the graph in more than one place.
4
x
-8
-4
4
8
-4
-8
-12
The relation is a function. The vertical-line cuts the graph in exactly one place.
y
Lesson 25 147