Example graphs

Six curves worth knowing by sight. Each page explains what the equation is doing, which features to look for, and where the shape turns up outside a maths classroom. Every graph opens in the calculator exactly as shown.

• Parabola

  The shape of every quadratic, and what each coefficient does to it.

• Sine wave

  The basic wave, its period and amplitude, and how cosine relates to it.

• Circle

  Centre, radius and why a circle cannot be written as y = f(x).

• Exponential curves

  Growth against decay, the horizontal asymptote, and why it never touches zero.

• Absolute value

  The V shape, where the corner goes, and how transformations move it.

• Rational functions

  Two branches, two asymptotes, and why the curve must not be joined across the gap.

Want the method rather than the example?

The guides work through each topic step by step.

• How to graph a parabola

  Standard, vertex and factored form, and how to read the vertex, intercepts and direction off each one.

• Finding intercepts

  What the intercepts mean, three ways to find them, and how to get exact values instead of estimates.

• Domain and range

  Reading both off a curve, writing them in interval notation, and the endpoint cases that cost marks.

All guides →