Question

Does the equation y=x represent a function?Explain why or why not.

Answer 1

yes because there is exactly one output for every input therefore the function is onto and one to one

Answer 2

Yes, the equation y = x represents a function.

Given equation:

• y = x

• To find: is given equation a function?

Explanation:

Which equation is classified as a function?

If that equation has an output variable and an input variable and if one unique input gives one and only one output, then that type of equation will be classified as an equation.

Proof that y = x is a function:

Assuming y to be output variable, and x to be input.

Now let y = x is not a function. Then there must exist one value of x for which there are two different outputs.

Let x = p be that value and let the outputs be y = a and y = b such that both are different.

Then we have:

$y = x\\a = p$

and

$y = x\\b = p$

From both equations,  we have a = b= p. Thus we have both a and b same. But we had assumed them to be different outputs, thus it is a contradiction. Thus, it is false that y = x isn't a function and thus y = x is a function as it outputs only one value to one input.

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