a If a relation is a function, how many y-values can an x-value have?
B
b If a relation is a function, how many y-values can an x-value have?
A
a
Function? No. Domain: -3≤ x ≤3 Range: -3≤ y ≤ 3
B
b
Function? Yes. Domain: -2≤ x ≤ 3 Range: -2≤ y ≤ 2
Practice makes perfect
a For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values.
Vertical Line Test
In a graph, we can check if each x-value has only one y-value by subjecting it to the vertical line test.
Observing the graph, we can see that there is at least one x-value with more than one y-value. The graph fails the vertical line test, so the graph is not a function.
Domain and Range
To determine the domain of this relation, consider which values of x the graph can take. In this case, the minimum x-value is -3 and the maximum x-value is 3. This means that the domain is all numbers between -3 and 3.
Domain: -3≤ x≤ 3
In the same way, the range of a relation is all values of y that the graph can take. In this case, there is a minimum y-value at y=-3 and the maximum y-value at y=3. Therefore, the range is all numbers between -3 and 3.
Range:-3≤ y≤ 3
b For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values.
Vertical Line Test
In a graph, we can check if each x-value has only one y-value by subjecting it to the vertical line test.
On the given graph, there is no visible part where two points have the same y-value. Each vertical line passes through the graph at only one point, so the graph is a function.
Domain and Range
To determine the domain of this relation, consider which values of x the graph can take. In this case, the minimum x-value is -2 and the maximum x-value is 3. This means that the domain is all numbers between -2 and 3.
Domain: -2≤ x≤ 3
In the same way, the range of a relation is all values of y that the graph can take. In this case, there is a minimum y-value at y=-2 and a maximum y-value at y=2. Therefore, the range is all numbers between -2 and 2.
Range:-2≤ y≤ 2
