Thread: Using transformations to write a function?

The function f, represented by f(x)=122.8x+786.2, models the average tuition at public four-year colleges from 1981 to 1994, where x is the year and x=1 corresponds to 1981. Use transformations to determine a function g that computes the average tuition at four-year colleges during the year x, where x is the actual year.

Need some guidance please?

Originally Posted by moomoo762

The function f, represented by f(x)=122.8x+786.2, models the average tuition at public four-year colleges from 1981 to 1994, where x is the year and x=1 corresponds to 1981. Use transformations to determine a function g that computes the average tuition at four-year colleges during the year x, where x is the actual year.

Need some guidance please?

Jus put 1981 at the place where x=1. I.E. relable your axis.

We can assume that g is a linear transform of f.

hence g=Af+B
where A,B are transformation constants.

Now determine A,B

Spoiler:

by definition of g,
f(1)=g(1981)=Af(1981)+B
by definition of f
f(1)=122.8(1)+786.2

hence,
Af(1981)+B=122.8(1)+786.2........(1)

Similarly,
Af(1982)+B=122.8(2)+786.2.........(2)

subtracting (1)from (2)
A(f(1982)-f(1981))=122.8
hence, A=1
B=243144