Building blocks

## Warm-up

In Mapping a function, we explored mapping diagrams for linear functions. What happens if we now compose two functions?

• How could we draw a mapping diagram to show the composition of the function $f(x)=\frac{3}{2}x$ with the function $g(x)=2x$ to get the function $h(x)=g(f(x))$?

• We described linear functions as scalings. How are the scalings represented by the three functions $f$, $g$ and $h$ related to each other?