how do draw your line for cubic function?

⚑ Flag

Do you mean, "How do I graph y = 1/2 (x - 4)^3 - 5 ?" or "How do I graph f(x) = x^3 ?" In either case, I usually plot points when I'm graphing functions. The key to graphing y = 1/2 (x - 4)^3 - 5 is knowing what the graph of its parent function, f(x) = x^3, looks like. So if you aren't familiar with the graph of f(x) = x^3, then I would start by graphing this function carefully on graph paper. Plot lots of points, for example, x = -2, -1, -0.5, 0, 0.5, 1, 2. This will get you familiar with the special shape of the cubic graph. I mention the cubic graph's "inflection point" in the video. For f(x) = x^3, the inflection point is (0,0). It's where the graph switches from curving to the right to curving to the left. When you are graphing transformations of f(x) = x^3, you still want to plot points, but you don't have to plot so many if you know that elementary transformations don't change the basic cubic shape. Transformations can stretch or compress the graph, reflect it or translate it. Usually, if you plot 3 to 5 points, including the inflection point, you'll get a very nice graph of a transformed cubic.