Question

Which of the following shows the graph of y = 2 l n x
On a coordinate plane, a curve starts at (0, negative 2) in quadrant 4 and then increases into quadrant 1 and approaches y = 3.
On a coordinate plane, a curve starts in quadrant 4 and then curves up into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0).
On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 1).
On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 2).

Answer 1

The second description. Reason: y = 2 ln x is defined only for x>0 so the curve is in quadrants 4 (for 0<x<1) and 1 (for x>1), it crosses the x-axis at (1,0) (since ln 1 = 0), and as x→0+ it goes down toward −∞ (vertical asymptote at the y‑axis). The other choices incorrectly show a y‑intercept or a finite horizontal asymptote.