Question

Use the image to answer the question.

Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
▼Click for Long Desc
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 (1,3)
, 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 (3,1)
, and the translated function is y=f(x+2)
.

Answer 1

(3, 1) and y = f(x − 2).

The solid curve (zero at x=0) is shifted right 2 to match the dotted curve (zero at x=2), so the point (1,1) moves to (3,1) and the rule is y = f(x−2).