Question

Given the graph below, which of the following statements is true?

The graph represents a one-to-one function because every x-value is paired with only one y-value.
The graph represents a one-to-one function because it is defined for all x-values.
The graph does not represent a one-to-one function because it does not pass through the origin.
The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
Mark this and return

Answer 1

Option d is right

Explanation:

A function is called one to one if two x will not have same y value.

In other words, in the domain each x is matched with a unique y and if x1 not equals x2 we have the corresponding y1 will not be equal to y2.

In the graph given, we find that the y value say 1 has preimages in both to the right of y axis and to the left of y axis.

Hence this is not one to one.

This is a function because each x has a unique image. If we draw a vertical line in any part of the graph we find that it cuts only one time the graph of f(x)

Hence f is a function but not one to one. A one to one function need not pass through the origin.

Hence we find that of the options given, a,b and c are wrong.

But option d is right.