Question 0119

Sketch the graph of ${y=\left| \mathrm{e}^x - 7 \right|,}$ giving the exact values of any points where the curve meets the axes.

Without using a calculator, and showing all your working, find the exact interval, or intervals, for which ${\left| \mathrm{e}^x - 7 \right| \leq 5.}$ Give your answer in its simplest form.