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

The translated function is y = log(x − 1) − 2. So the graph must have a vertical asymptote at x = 1 and pass through (2, −2) (since (1,0) on y = log x moves to (2, −2)) and rise to the right into quadrant I. That matches the fourth choice: "starts at (1, −3) and curves up into quadrant 1."