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}