Exercise 1 : Draw a graph that does not correspond to a function

This graph doesn't represent a function.

Hi Dbg,  

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.  

COOL! Why is it important to know this?

What does it mean mathematically?

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.....

Thanks Chris, of course Chris is correct :)

The derivative cannot be expressed as a function of x but it can certainly be expressed as a function of y.

Ok so why is such a bid deal made of functions verses non function ?