Question

Which is the graph of y = negative log (x minus 2) + 3?
On a coordinate plane, a curve starts at (2, 0) and curves up and goes through (3, 3) and (9, 5).

On a coordinate plane, a curve starts at (2, 6) and curves down and goes through (3, 3) and (10, 2).

Answer 1

The second graph.

Reason: y = −log(x−2)+3 has a vertical asymptote at x = 2 and is decreasing for x > 2 (the minus sign flips the usual increasing log). Also log(3−2)=log 1 = 0 so y(3)=3, and for x=10 y ≈ −log(8)+3 ≈ 2.10, so the curve is high near x=2 and falls through (3,3) toward about (10,2). That matches the second picture.