Question

Use the image to answer the question.

Two lines are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 2 to 2 in increments of 1.
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A dotted line passes through the points left parenthesis negative 2 comma 1 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The solid line passes through the points left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.

The graphs of the functions f(x)=12x
(solid line) and g(x)=f(x)+2
(dotted line) are shown. How does adding 2 to f(x)
impact the graph?

Option 1: It translates the graph of f(x)=12x
up 2 units.

Option 2: It translates the graph of f(x)=12x
down 2 units.

Option 3: It reflects the graph of f(x)=12x
over the x
-axis and translates it up 2 units.

(1 point)
Option

Answer 1

Option 1.

Adding 2 to f(x) shifts every y-value up by 2 units (e.g. f(0)=0 → g(0)=2, f(-2) = -1 → g(-2)=1), so the graph is translated up 2 units.