Draw the graphs and find the points of intersection of x and x^3

by RoRi

July 13, 2015

Let $f(x) = x$ and $g(x) = x^3$ . Draw the graphs of $f$ and $g$ and show the points at which they intersect.

First, we can determine algebraically the points of intersection. They are the points such that $f(x) = g(x)$ , i.e.,

$x = x^3 \ \implies \ x = 0 \quad \text{or} \quad x^2 = 1 \ \implies \ x = 0,\pm 1.$

The function values at these points are,

$f(0) = g(0) = 0, \quad f(-1) = g(-1) = -1, \quad f(1) = g(1) = 1.$

Thus, the points of intersection are $(0,0), (-1,-1), (1,1)$ . The graph is below.

Rendered by QuickLaTeX.com

Stumbling Robot