3.4.2 A multiplicative function

Next: 3.4.3 The function as Up: 3.4 Examples of functions Previous: 3.4.1 The constant function

3.4.2 A multiplicative function

Another function that most are familiar with is a multiplicative function that relates quantity of gas purchased at the gas station to the total cost of filling up. For example if gas is priced at $1.07/gallon, then we have the following rule for determining the total cost:

Here's a diagram that shows this relationship

$\begin{picture}(10,10) \put(1,4){\vector(1,0){7}} \put(1,5){\textcolor{blue}{Gal... ...,4){\vector(1,0){6}} \put(15.25,5){\textcolor{green4}{Total cost}} \end{picture}$

$\begin{picture}(17,1) \put(0,1){\it Units:} \put(2,1){ \textcolor{blue}{Gallons}... ...{ \textcolor{red}{\$/Gallon}} \put(16.5,1){\textcolor{green4}{\$}} \end{picture}$

Written mathematically, we have Cost = f(gallons), where f is the function that multiplies the number of gallons by 1.07.

At Wharton, we will stress the practical interpretation of any concept covered. In the above example it is very useful to recognize that all the quantities in the equation have units attached. For example, x is the number of gallons and y is the cost in dollars. It follows that in order to make the equation balance (the units on the right hand side must be the same as the units on the left hand side), the multiplicative factor must be measured in dollars per gallon.

Next: 3.4.3 The function as Up: 3.4 Examples of functions Previous: 3.4.1 The constant function

Richard Waterman
1999-04-30