How do you decide whether the relation #x = y²# defines a function?
1 Answer
We can graph the relation and do the vertical line test.
Explanation:
Whenever we have to check if a relation is a function, we draw its graph and do the vertical line test.
The vertical line test says that if a vertical line touches the graph once, the relation is a function. And if the vertical line touches the graph more than once it's not a function.
Example
Let's graph this relation.
graph{sqrtx [-10, 10, -5, 5]}
Now if we draw a vertical line we can see that the line touches the graph at only one point everywhere.
Therefore it is a function.
Additional
A Line, Parabola etc. are functions because they pass the vertical line test.