Question

What is the parent function of: `f(x)=2(1/2)^-x-12` ?

Answer 1

`color(red)(f(x)=2^x)`

Explanation:

A parent function is the simplest form of a function that preserves the "shape" of a given function.

By this we mean that the given function can be converted into the given function by shifting or stretching the parent function.

Given
`color(white)("XXX")f(x)=2(1/2)^(-x)color(magenta)(-12)`
we can see that the `color(magenta)(-12)` is simply a shift of `f(x)=2(1/2)^(-x)` (down `12` units)

Further, considering
`color(white)("XXX")f(x)=color(green)2(1/2)^(-x)`
we can see that the `color(green)2` is a simple stretch of the function `f(x)=(1/2)^(-x)`

Finally, if we remember that `a^(-b)=1/a^b`
then we see that we can simplify our parent to
`color(white)("XXX")f(x)=2^x`

Note that it might be argued that this can be further simplified by replacing `2` with any constant greater than `1`, but his seems pointless to me.