A reflection about the x-axis and a dilation of 1/2. y=4^x

y = -.5 * 4^(2x)

Step-by-step explanation:

A reflection about the x axis is basically mutliplying the whole function by -1, so -1 * f(x)

I assume a dilation means relative to the origin, so in other words thngs are half as far away from the origin.  taking a super simple ne, x^2 would normally have a point at (1,1) we want half that so (.5,.5)  similarly (2,4) would become (1,2).  The method to do this is to make both horizontal and vertical stretches be 1/2.  a vertical stretch is a*f(x) where a gives a stretch of a, so we want a to be .5.  a vertical streth is f(bx) [or f(b(x-c)) if there is a horizontal shift as well] where the horizontal stretch is 1/b.  So to get .5 we want b to be 2 so the stretch is 1/2.  so together we need .5*f(2x) [or .5*f(2(x-c) if there were a horizontal shift.]  

Putting the reflection and dilation together gets us  -.5*f(2x) Since your problem does not mention any horizontal shifts.

Now, your problem is specifically f(x) = 4^x.  Soreplace all x with 2x and stick -.5 out in the front.

y = -.5 * 4^(2x)

b

step-by-step explanation:

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: