Curve tracing

Curve Sketching

		Symmetry

		A curve is symmetric with respect to:

		1. The x axis, if its equation is unchanged when y is replaced by -y, that is, f(x) = y and f(x) = -y both hold.

		2. The y axis, if its equation is unchanged when x is replaced by -x, that is f(-x) = f(x).

		3. The origin, if its equation is unchanged when x is replaced by -x and y by -y, simultaneously, that is, f(-x) = - f(x).

		4. The line y = x, if its equation is unchanged when x and y are interchanged, that is, y = f(x) implies x = f(y).

		Intercepts

		An intercept is a point on either axis of a coordinate system where the curve of a function passes through or intercepts. The x intercepts are obtained by setting y = 0 in the equation for the curve and solving for x (when possible). The y intercepts are obtained by setting x = 0 and solving for y.