# Function Mathematics and the aMAZEing Math Maze

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Here we are, you did a search for Function Mathematics or you have successfully moved ahead in the aMAZEing Math Maze.  We'll talk about functions later - let's get into the maze for now.

## The aMAZEing Math Maze Q15

This question is vaguely about rabbits.  There's kind of a neat article that explains that one rabbit can turn into 184,597,433,860 rabbits in seven years.  But, I digress....

Bob, decided to breed rabbits for fun and profit.  By his calculations, his rabbit population would triple every month.  I know - a bit unrealistic to start with 1 rabbit (ask your parents - jk). What type of function would represent this data?

a)  Linear

c)  Exponential

d) Absolute Value

## Function Mathematics

O'k, here's the skinny on Function Mathematics.  A problem is a function when each value in the Domain links up with only one value in the range.  The Domain is the values you can put into the equation, and the Range is the output.  So, let's look at the equation y = mx +b.  m is the slope, and b is the y intercept (when x = 0 all we have left is y = b and that's where the line intercepts the y axis.

x is said to be the independent variable, because we can make it be just about any value we can think of.  We choose a value for x and that determines the value of y.  y is said to be the dependent variable because it's value depends on what value we give to x.

Now, the domain (in this case) are the values we can give to x and the range is all the values can end up giving to y.  The equation is a function if every value of x yields only one value of y.  Two or more of the x values can point to the same value of y, but no value of x can point to two different values of y - if they do, then it's not a function.

## That made no sense at all!

Let's try this another way.  If you graph the equation, you can use the "vertical line test".  This says that for the equation to represent a function, no matter where you draw a vertical line, it will not cross the line formed by the equation more than once.

## Still don't have it?  One more try ....

In a standard equation, no one value of x will yield more than one value of y.