SL 2.3—Graphing functions

A graph shows how outputs depend on inputs. A useful sketch preserves key behaviour—intercepts, turning points, asymptotes, end behaviour and domain—not every plotted pixel.

Start with the domain and scale, then find features that determine the shape. Use a calculator or points to check the sketch, but interpret the graph rather than copying an unlabelled screen.

For y=(x−2)²−1, the vertex is (2,−1), the x-intercepts are 1 and 3, and the parabola opens upward. Those three facts are more informative than a dense table of values.

A sketch need not be to scale, but it must not invent features. Distinguish an intercept from a turning point and do not ignore a restricted domain.

A 'draw' should be accurately plotted, while a 'sketch' preserves essential features. Label both axes, units and key coordinates. Technology can graph $f+g$ or $f-g$ pointwise: if $f(x)=x^2$ and $g(x)=2x$, then $(f-g)(x)=x^2-2x$; its zeros at 0 and 2 are where the original graphs intersect because $f(x)=g(x)$.