A function is a value whose size depends on the size of another value. For example, the number of miles you can travel in your automobile is a function of the number of gallons in your gas tank. Or, in traveling on a trip 100 miles, the number of miles remaining to be traveled is a FUNCTION of the number of miles you have already traveled.
As you can see in the above examples sometimes functions increase as the related value increases (the more gallons of gas you have, the further you can travel).
And in another case: As the function gets smaller, the related value gets larger. (The distance that you still have to travel on your trip becomes smaller as the distance that you have traveled becomes greater).
Okay! So the functions we are talking about are two related mathematical values. That is, the size of one depends upon the size of the other. So, how are functions important in solving right triangle problems? Let's find out: