Question

I am really confused about this question for math.. any help would be really appreciated:

A reflection about the x-axis and a dilation of 2. y= (1/4) to the power of x

Answer 1

`y= (\frac 1 4 )^x`

A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so

`y'= -y = - (\frac 1 4)^(x')`

A dilation of 2 is the mapping (x'',y'')=(2x', 2y')

So

`x'=x''/2, y'=y''/2`

`y''/2= - (\frac 1 4)^(x''/2)`

`y'' = - 2((\frac 1 4)^(1/2))^(x'')`

`y''= - 2(\frac 1 2)^(x'')`

We can rewrite that without the primes and combine the powers of 2.

`y = - 2^(1-x)`

Let's graph these and see if we're close,

Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}