Section 1.10 : Common Graphs
4. Without using a graphing calculator sketch the graph of \(f\left( x \right) = \ln \left( x \right) - 5\).
Recall the basic Algebraic transformations. If we know the graph of \(g\left( x \right)\) then the graph of \(g\left( x \right) + c\) is simply the graph of \(g\left( x \right)\) shifted down by \(c\) units if \(c < 0\) or shifted up by \(c\) units if \(c > 0\).
So, in our case if \(g\left( x \right) = \ln \left( x \right)\) we can see that,
\[f\left( x \right) = \ln \left( x \right) - 5 = g\left( x \right) - 5\]and so the graph we’re being asked to sketch is the graph of the natural logarithm function shifted down by 5 units.
Here is the graph of \(f\left( x \right) = \ln \left( x \right) - 5\) and note that to help see the transformation we have also sketched in the graph of \(g\left( x \right) = \ln \left( x \right)\).
