Draw the graph of \(y=3^x\) for values of \(x\) from \(-2\) to \(+2\), plotting at least nine points. [Take \(\quantity{2}{cm}\) as unit on the axis of \(x\), and \(\quantity{1}{cm}\) as unit on the axis of \(y\).]

Use your graph to find

  1. the roots of the equation \(3^x=3x+2\),
  2. the range of values of \(k\) for which the equation \(3^x=kx\) has no real roots.

Can you think of a way to consider the equation \(3^x=3x+2\) in terms of two intersecting curves?

Can you use the graphs you sketch to help solve this equation?