Guides

Each guide walks through one topic with worked examples and real graphs. Every figure is a live graph you can open in the calculator and change, so you can test what happens rather than take our word for it.

Graphing functions

• 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.

• Piecewise functions

  Restricted domains, open versus closed circles, and why a jump should never be joined up.

• Asymptotes

  Finding all three kinds, why the curve breaks at a pole, and telling a hole from an asymptote.

Data, systems and trigonometry

• Linear regression

  Line of best fit, what r and R squared actually tell you, and when a linear model is wrong.

• Graphing inequalities

  Shading the right side, dashed versus solid boundaries, and finding a feasible region.

• Sine and cosine graphs

  Amplitude, period, phase shift and midline, each one isolated so you can see what it does.

• Systems of equations

  Reading intersections exactly, and recognising no-solution and infinite-solution systems.

Example graphs

Short pages built around one curve each, with the equation explained and the graph ready to open.

• 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.

Using a TI-84

Keystroke references for the physical calculator, for when the exam does not allow anything else.

• TI-84 graphing guide

  Exact keystrokes for entering a function, setting the window, and using the CALC menu.

• TI-84 linear regression

  Entering lists, running LinReg, and turning on the r value that is hidden by default.

• Calculators on the SAT and ACT

  What each exam board allows, what is banned, and how to practise online without a nasty surprise.