SL 2.4—Key graph features

Key graph features translate a picture into statements: intercepts show zeros or initial values, a gradient shows rate of change, a turning point marks a local extreme, and an asymptote describes a value the graph approaches.

Read the axes and units first. Then connect the feature to the context: a maximum may be a capacity or peak, while a negative gradient may represent decline. A graph can show association without proving why it occurs.

If a concentration curve levels off at 8 mg L⁻¹, the horizontal tendency suggests a limiting value; it does not prove the process has stopped or that 8 is a universal constant.

Do not confuse a horizontal tangent with a horizontal asymptote. Check whether the statement concerns one point, a local interval or long-run behaviour.

Feature checklist: $x$-intercepts are roots or zeros, the $y$-intercept is $f(0)$, and a quadratic vertex lies on its axis of symmetry. Record local maxima/minima, vertical and horizontal asymptotes, and any graph symmetry. To find the intersection of two curves with technology, graph both and solve $f(x)=g(x)$, then report the common point and verify it satisfies both equations.