Evaluate this piecewise function at x=-4 and x=4. (can someone show me how to solve this because i don't know what to do to solve this)

The piecewise function is
f(x) = x²,   x≤ -4
      = x³,  -4 < x ≤ 1
      = √x,  x > 1

To find f(-4), we note that f(x) = x²,   x ≤ 4, so we should use this part of the function.
f(-4) = (-4)² = 16

To find f(4), we note that f(x) = √x, x > 1, so we should use this part of the function.
f(4) = √4 = +2 or -2.
A graph of the function is shown below. It indicates that f(4) = +2 for continuity.

 
f(-4) = 16
f(4) = 2.