Q.Express the area $A$ of a circle as a function of its diameter $d$.

Recognise each curve's shape: an S-shaped curve is the cube function, a two-level step is the piecewise sign-type function, a straight line through the origin at 45 degrees is the identity function, and a two-branch curve hugging the axes is the reciprocal function.

• Graph (a) is a smooth, origin-symmetric S-shaped curve rising steeply -- this is the cubic $f(x)=x^3$, i.e. definition (ii).
• Graph (b) is a two-level horizontal step, $y=1$ for $x>0$ and $y=-1$ for $x<0$ -- this matches the piecewise function equal to $1$ for $x>0$, $0$ at $x=0$, $-1$ for $x<0$, i.e. definition (iv).
• Graph (c) is a straight line through the origin with slope $1$ -- the identity function $f(x)=x$, i.e. definition (iii). …