## Functions and Graphing: When Students Ask

• Why do I need to know about graphing integers?
Graphing integers is a way to visualize relationships between two variables. By looking at graphs, statisticians, scientists, engineers, and economists can make decisions and predictions.
• What is a function, and when will I use one?
A function is a rule that associates one and only one value of one variable with each value of another variable. Functions are encountered everywhere. For example, if your local bank pays 4% simple interest per year on money invested, then the function can be given by the formula I = 0.04p, where I is the interest earned in one year on the principal, p, invested. If hamburgers cost \$1.99, then the amount you pay in dollars, d, for h hamburgers is given by d = (1.99)h. Both of these formulas are functions. There are many other everyday situations which can be represented by functions, such as the amount, a, you pay for t tickets to a play at \$10.00 per ticket (a = 10t), the distance d you would travel on your bike in h hours if you average 12 miles per hour (d = 12h), or the length in inches l for a rope c centimeters long (l = c/2.54).
• Why is the order of operations important?
If we didn't agree on the order of operations and then evaluated 2 + 4 x 5, some people might add first to get 6 and then multiply to get 30. Other people would multiply first to get 20 and then add to get 22. Actually, there are calculators that evaluate this same expression in different ways when the stroke sequence of 2 + 4 x 5 = is entered. Scientific calculators give an answer of 22, which is the one we get using the order of operations.