Question

The function y = log (x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
On a coordinate plane, a curve starts at (negative 1, negative 5) and curves up into quadrant 1. It approaches y = 1.
On a coordinate plane, a curve starts at (1, negative 4) and curves upwards. It approaches y = negative 1.
On a coordinate plane, a curve starts at (negative 1, negative 1) and curves up into quadrant 1. It approaches y = 5.
On a coordinate plane, a curve starts at (1, negative 3) and curves up into quadrant 1. It approaches y = 5.

Answer 1

Translating 1 unit right and 2 units down gives
y = log(x - 1) - 2.

Key features: domain x > 1 (vertical asymptote x = 1) and the graph passes through (2, −2) because log(2−1) − 2 = 0 − 2 = −2.

So choose the graph that has a vertical asymptote at x = 1 and curves upward into quadrant I, passing through (2, −2). (That is the graph described by the option that begins at x = 1 and curves up into quadrant I — option D.)