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?