Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically

Sketch the curve \(y=2-{{\mathrm{e}}^{3x}}\) for all real values of \(x\), showing clearly on your diagram the coordinates of any points of intersection with the \(x\)- and \(y\)- axes.

Find the equation of a suitable straight line that can be drawn on the graph of \(y=2-{{\mathrm{e}}^{3x}}\) to obtain a solution of the equation \(x=\ln \sqrt[3]{4-x}\).