If given a function, how do I graph it without a calculator?

Question

Take this for example, f(x)=(x^(2/3))((6-x)^(1/3))

What steps would I take to graph this?

Answer 1

compute y = f(x) for several values of x and plot the (x,y) pairs. you might simplify f(x) a little first:

f(x) = [x²(6-x)]^(1/3) = [6x² - x³]^(1/3)

Answer 2

You can find some interesting points, 0, 1, 2, -1, -2, etc. and solve f(x) for those values. Then graph what you find. You should see a curve (or two or three) emerge.