Answer:
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)
