#'s 3 and 8

3. Find and simplify the Df(x) when f(x)=(2x+1)^2. First find f(x+h)-f(x), which is (2(x+h)+1)^2-(2x+1)^2= (4x^2+8hx+4x+4h^2+1)-(4x^2+4x+1). The 4x^2, 4x, and 1 cancel out so your left with 8xh+4h^2+4h. Then you take that all over h and the h's cancel out so you're left with 8x+4h+4.

8. First look at the original graph and see how x changes. x changes from 2 to 3 and from -2 to -3 which means x was scaled by 1.5, but you have to write it as the reciprocal, so part of the equation becomes abs(3/2x). Then you see how y changed. y went from 2 to 1 and from -2 to -1 so y was scaled by 1/2. So the rest of the equation is abs(2y), so the entire equation is abs(2/3x)+abs(2y)=2. You can always chack it by putting in values for x and y.