Exercise 1 : Draw a graph that does not correspond to a function
Jdh3010's graph is NOT a function because it does not pass the vertical line test.
When you draw any vertical line through a function it can cross the fuction in AT MOST one place.
This graph would often have two crossing points :)
This means that some x values have more than one y value.
If a graph or an equation is a function it means that no x value can have more than one y value.
Well off the top of my head I will say that only a function can be differentiated. So it is very important for calculus. AND calculus is an immensely important branch of mathematics.
I don't want to disagree with Melody here, but the graph in the first answer is something like x = y^2 - 5....and this can definitely be differentiated as 1 = 2yy' → y' = 1/2y ....the derivative doesn't exist for y = 0.....it is positive for y > 0 and negative for y < 0
Modeling real-life situations by the use of functions is a very important tool in mathematics......here....we have "function" of y rather than a function of x.......this is not common...but it can occur.....