Question

Y=x sketch the graph and determine is it a functions

Answer 1

Yes it's a function

Answer 2

You can determine if a curve or line represents a function in one or more ways. Graphically you can apply the vertical line test. This is a test wherein you look at the graph and determine if there is any point in the domain when you draw a vertical line and see if it hits more than one point on the graph.

This is akin to the concept that a function represents that there is only one output for every one input. For every input (x) there is only one output (y or f(x)) in a function.

In your graph, there is no point on your graph where if I draw a vertical line it will touch more than one point. This means we have a function.

f(x) = x or how you say (y = x) is a very common function and comes up a lot in mathematics.