How Do I Deal With Variables Other Than x in Linear Functions?

When working with functions with unusual variable names and scaling, students often run into two problems.

  • trouble with what each variable represents
  • trouble with the scaling of the variables

Since we rarely use x in Finite Math to represent the independent variable, we need to get used to these names. Typically, the variables are aligned or scaled. This means we need to pay particular care to interpreting answers.

In one type of the problem, you are given a demand function $latex \displaystyle p=D(q)=32-1.25q$ where p is the price in dollars and q is the quantity of watches demanded in hundreds. In part b, you were asked to find the price when the demand is 800 watches. This quantity corresponds to $latex \displaystyle q=8$ and gives a price of

$latex \displaystyle D(8)=32-1.25(8)=22$

Notice how the scaling on the variable works…800 watches is input as 8 hundred. In part c, you need to find the demand when the price is 27 dollars. Now we know the output from the function and we need to find the corresponding input,

$latex \displaystyle 32-1.25q=27$

When we solve this for q we get $latex \displaystyle q=4$. In other words, 4 hundred watches are demanded when the price is 27 dollars. Since the units on the answer blank is watches, you will need to type 400 in the answer blank. I think many of you were not taking the units into account on this problem. Units are incredibly important in the real world where you are dealing with millions of dollars. In those cases misinterpreting 2,000,000 dollars and 2 million dollars may cost you your job.