The equation f(x)=x is known as the__?

Answer 1

This is the identity function.

It gets its name because it has similar properties to the additive identity (0) and the multiplicative identity (1).

Answer 2

This is an open ended question. Here are my thoughts (in a random order but equally ranked) with justifications.

(A) f(x) = x is known as the linear function, because the graph of this function, is a straight line.

{ However, we need not graph to say this is linear- We can say it is linear by looking at the highest exponent for the input variable in the equation. Please check this: f(x) = x-2 , g(x) = 3x -5 are all equations of linear functions.}

(B) f(x) = x is known as the identity function, because if we input x to this function, then the output is also x, which means that the output is always identical (same as) to the input.

I encourage you to make a table. x is the input and f(x) is the output. If you enter –1 as your input, then based on this function equation f(x) =x, te output is also –-2 ; if you enter a zero for the input x, then the output f(x) must be zero , so on and so forth.

(C) f(x) = x is an odd function , because it is symmetric with respect to the origin .

(D) f(x) = x is a 1-1 function because each input has an unique output. {If you did the graph, the vertical line test must ring a bell !)