Question

A common use of transformations is to take the units used in one model and change them to other units. For example, suppose that we have a function, f(x), that models a company’s profits in hundreds of thousands of dollars in terms of hundreds of units produced, x. (a) Use transformations to find the function that will give the profits as hundreds of thousands of dollars in terms of units produced.

Answer 1

f(x) is a function that models a company's profits in hundrends of thousands of dollars in terms of hundreds of units produced;
This means that f(x) is in terms of hundreds of thousands of dollards and 'x' is in terms of hundreds of units produced.
Now we are to find a function that will give the profits as hundreds of thousands of dollars in terms of units produced.
So 'x' which is in hundreds of units produced is to be broken down into single units produced;
Let number of units be = t;
We know that x=100 t
f(t) = f(100x)
So replace 'x' in f(x) equation with 100 't' and you will have an equation f(t) that gives profits in hundreds of thousands of dollars in terms of the number of unit sproduced 't'