Combining a Shift and a Stretch

Remember: what happens inside parentheses happens first. First, we move the graph left 2 units, then stretch the function vertically by a factor of 5, as in Figure 12. The vertical asymptote will be shifted to $x=\mathrm{-2.}$ The x-intercept will be $(\mathrm{-1,}0).$ The domain will be $\left(\mathrm{-2},\infty \right).$ Two points will help give the shape of the graph: $(\mathrm{-1},0)$ and $(8,5).$ We chose $x=8$ as the x-coordinate of one point to graph because when $x=\mathrm{8,}$ $x+2=\mathrm{10,}$ the base of the common logarithm.

Figure 12

The domain is $\left(-2,\infty \right),$ the range is $\left(-\infty ,\infty \right),$ and the vertical asymptote is $x=-2.$