Question

Choose the best descriptor for the graph of f(x) = ln(x - 5).


a. It increases rapidly, goes through the point (5,1), then increases gradually.
b. It increases slowly, goes through the point (5,1), then increases rapidly.
c. It increases slowly, goes through the point (6,0), then increases gradually.
d. It increases rapidly, goes through the point (6,0), then increases gradually.

Answer 1

D.

To get an intuition: http://fooplot.com/plot/1vfpzakasr

Also, at \(x=6\), we have \(\ln(6-5)=\ln(1)=0\) since: \(e^0=1\), and the graph tends down to \(-\infty\) as \(x\to5\), since \(\ln(0^+)\) (Very near zero, on the positive end) tends to negative infinity.

Answer 2

thank you so much!!