a For what x- and y-values does the graph exist? When is a relationship a function?
B
b For what x- and y-values does the graph exist? When is a relationship a function?
C
c For what x- and y-values does the graph exist? When is a relationship a function?
A
aDomain: All real numbers
Range: All real numbers Function? Yes
B
bDomain: All real numbers
Range: Not all real numbers Function? Yes
C
cDomain: Not all real numbers
Range: All real numbers Function? No
Practice makes perfect
a Let's first identify the domain and range, then determine if the relation is a function.
Domain
The domain describes the possible x-values of a graph. Examining the diagram, we see that there are no restrictions when it comes to the x-axis. The graph goes from left to right with no interruptions, and it extends indefinitely in both the negative and positive directions.
Therefore, the domain is all real numbers.
Range
As for the range, it extends in the positive and negative vertical direction indefinitely, which means the range is all real numbers as well.
Is it a Function?
If the graph is a function, there is exactly one corresponding y-value for each x-value. By looking at the graph we can conclude that it is a function.
b Like in Part A, let's identify the domain and range first, and then determine whether it is a function.
Domain
Examining the diagram, we see that there are no restrictions when it comes to the x-axis. It goes from left to right with no interruptions, and extends indefinitely in both the negative and positive direction.
Therefore, the domain is all real numbers.
Range
Examining the diagram, we see that the graph extends indefinitely in the negative direction. However, in the vertical direction it does not extend beyond y=6, which is the graph's maximum value.
Therefore, the range can not be all real numbers, as we found a restriction in the values of y.
Is it a Function?
For each value of x there is exactly one corresponding y-value, so we can conclude that the graph is a function.
c Let's first identify the domain and range, and then determine whether the relation is a function.
Domain
The lowest value of x for which the graph exists is x=-2.
Therefore, the domain is not all real numbers, as we found a restriction.
Range
Examining the graph, we see that one part is pointing upwards and another is pointing downwards. Therefore, the range is all real numbers.
Is it a Function?
This graph is not a function, as there are values of x with 2 outputs. For example, if we draw a vertical line through x=2 we get two corresponding y-values, y=3 and y=1.
