Question

The solid curve starts from left parenthesis 1.3 comma 5 right parenthesis, then touches origin and goes down to left parenthesis negative 1.3 comma 5 right parenthesis. The dotted curve starts from left parenthesis 3.3 comma 5 right parenthesis, then touches x-axis at 2 and goes down to left parenthesis 0.7 comma negative 5 right parenthesis.

The original function y=f(x)
in the graph (solid line) goes through the point (1,1)
and is translated using a horizontal translation. Where is this point located after the translation, and what is the translated function?

(1 point)

The point is located at (3,1)
, and the translated function is y=f(x−2)
.

The point is located at (1,1)
, and the translated function is y=f(x−2)
.

The point is located at (3,1)
, and the translated function is y=f(x+2)
.

The point is located at (1,3)
, and the translated function is y=f(x−2)
.

Answer 1

Choose: The point is located at (3,1), and the translated function is y = f(x − 2).

Reason: the graph is shifted right 2 units (origin to x=2), so x is replaced by x−2; (1,1) moves to (1+2,1) = (3,1).