Question

Which graph does it represent a function?

Answer 1

The graph in the bottom right (The circle) is not a function

Explanation:

As the circle has multiple y values for each x value, it is not a function. In other words, that graph fails the vertical line test.

Answer 2

IV graph

Explanation:

Function: It is relation between x and y.For each x, there is a unique value of y.

Only one output for one input.

One value of x cannot have more than one images.

Vertical line test:

When we draw a vertical line passing through any given value of x and cut the curve more than one points then, the curve does not represents the function.

When a vertical line cuts the curve at one point then, the curve represents the function.

In I graph, We can see that

Image of 1 is 2.

Image of 2 is 1.

Image of -2 is 1.

There is only one output for input.

Hence, it represents the function.

In II graph,

By vertical line test, when we draw a vertical line x=1 then it cuts the graph at one point only.

Hence, it represents the function.

In III graph,

Image of 1 is 1.

Image of 0 is 2.

Image of -1 is 3.

Image of -2 is 4.

There is only one output for 1 input.

Hence, it represents the function.

In IV graph,

When we draw a vertical line x=1 then , it cuts the curve at two points.

Therefore, given circle does not represents the function.