Domain, Range & Transformations
📋 What it is
Domain is the allowed inputs; range is the possible outputs; transformations shift or stretch the graph.
🗣️ Coach says
Analysing a function means knowing its limits and moves. Domain = which inputs are allowed; range = which outputs can appear. Transformations slide or stretch the whole graph — adding 3 lifts every point up 3.
🧠 Memory hook
Domain = inputs allowed. Range = outputs possible. "+3" lifts the whole graph up by 3.
😂 Giggle
Why was the linear function so reliable?
It always went in a straight line — no surprises!
😲 Whoa!
Video game designers transform functions constantly — shifting and stretching curves to make a jump feel just right.
✅ Quick check: For a function f(x), what does the "domain" describe — the inputs or the outputs?
Say your answer out loud first — then reveal.
The inputs — the set of x-values you're allowed to put in.
Domain is the input set; range is the output set.
🧪 Try it! (2 minutes)
Take "x + 0" and change it to "x + 3". Every output rises by 3 — that's a transformation.