SL 2.3—Graphing functions

Sketch a graph from structure and context.

Use intercepts, turning points, asymptotes, scale and context to sketch the shape before relying on a calculator.

Worked example
A revenue graph crossing the x-axis at 0 and 100 has break-even intercepts; label what each axis means.

Worked example
What makes a sketch usable? labelled axes and key features, not artistic smoothness.

Common boundary
A calculator trace without scale or labels is not a mathematical interpretation.

Sums and differences are graphed pointwise: if $f(x)=x^2$ and $g(x)=2x$, then $(f+g)(x)=x^2+2x$ and $(f-g)(x)=x^2-2x$. Generate or sketch each new function, then label axes, intercepts, extrema and any context-specific units. Do not add the visual heights without first checking both functions share the same input domain.