Question

# Determine whether each graph represents a function ?

Hint:

### We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point. We use this method to check if each of the given graphs represent a function.

## The correct answer is: not a function

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

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