Question

How do you write an equation in the form f(x) = kx^n for the direct variation functions given f(2) = 8 and n = 4?

Answer 1

`f(x)=kx^n` is not a direct variation function

Explanation:

If `f(x)` were a direct variation function replacing `x` with a multiple of `x` would result in the value of `f(x)` being multiplied by that same multiple.
To be a direct variation `f(a*x)=a*f(x)`

However,
if the intended question was simply to fin the value of `k`
given
`color(white)("XXX")f(x)=kx^n`
and
`color(white)("XXX")f(2)=8` when `n=4`
then
`color(white)("XXX")f(2)=k*(2^4)=k*16=8`
`rArr k=1/2`