Today is rung 6 of 7 on this topic
Functions, notation, domain and range
Can do: Uses function notation confidently and states domain and range from a graph or a context.
Why it matters
Function language is the vocabulary of every remaining maths course. Domain restrictions are where context and algebra meet.
What it looks like when it's wobbly
Gives domain and range as memorised intervals without reference to what the variable represents.
⏱️ Two-minute check
"f(x) = √(x − 3). Domain? If f models the height of a ball, what's the sensible domain?"
Solid looks like: x ≥ 3 algebraically, and a context-restricted answer for the ball.
The full activity for this topic · 25 minutes
Domain in the Real World
- 1Take a real situation — ticket cost by number of people, water in a draining tank.
- 2Write the function, then ask what inputs actually make sense.
- 3Graph it and shade the part of the graph that's meaningful.
- 4Do a purely algebraic domain question — square roots and denominators.
- 5Compare: the algebra allows more than the situation does.
If it's too hard
Read domain and range off a given graph.
If it's too easy
Piecewise functions and their domains, and interpreting a discontinuity in context.
Say this
"The algebra allows that value. Does the actual situation? Can you have −2 people?"