Using Calculators for Graphs, Equations & Inequalities

Quick Summary

• You can type any function into your GDC as f(x) = and it will draw the graph for you — no table of values needed in the exam.
• The "analyze graph" / G-Solv menu finds roots (x-intercepts), maximum/minimum points, and intersections automatically.
• Solving f₁(x) = f₂(x) graphically just means: draw both graphs, find where they cross, and read off the x-coordinates.
• Solving f(x) = 0 is a special case — it's just finding where the graph crosses the x-axis (y = 0).
• Solving f(x) = k means finding where the graph crosses the horizontal line y = k.
• To solve an unfamiliar equation using a graph you've already drawn, rearrange it so one side matches your original function.
• For inequalities, solve the "=" version first to find the crossover points, then check which curve is on top in each region.
• When sketching from your GDC onto exam paper: freehand smooth curves, no ruler, mark all key coordinates.

1. Using Calculators to Sketch Graphs

Getting a graph onto your screen

Every GDC has an "Add Graphs" (or "Graph Mode") screen with a line that says f(x) = — sometimes labelled f1(x) = or Y1:. Whatever the label, the idea is identical: you type in the for your function, and the calculator plots every point that satisfies it.

Think of it like this — the calculator is testing thousands of x-values in a split second, working out the matching y-value for each one, and joining all the dots into a smooth curve. That's exactly what you'd do by hand with a table of values, just millions of times faster.

Don't skip the zoom step! A graph can look like a flat line or be totally off-screen if the window (the visible x and y range) isn't set sensibly. The "zoom-fit" button is your best friend here — it automatically finds a window that shows off all the key features (turning points, intercepts) without you guessing numbers.

Finding key features on the graph

Once your curve is on screen, go into the "analyze graph" menu (sometimes called G-Solv). This is where the real power is — instead of calculating things algebraically, you're asking the calculator "show me the interesting points."

turning points vertex

2. Using Calculators to Solve Equations

The core idea: intersections = solutions

x² + 3x + 1 = 2x + 1

• y = f₁(x) = x² + 3x + 1

cross