Which of the following equations is represented by the graph?

A.

f(x)=|x+3|+2f(x)=|x+3|+2

B.

f(x)=|x+3|−2f(x)=|x+3|-2

C.

f(x)=|x−3|−2f(x)=|x-3|-2

D.

f(x)=|x−3|+2f(x)=|x-3|+2


To determine which equation corresponds to the graph, we need to analyze the key characteristics of the given equations and understand how transformations of the absolute value function affect the graph. The general form of an absolute value function is:

\[
f(x) = |x - h| + k
\]

Where:
- \( h \) represents a **horizontal shift**: if \( h > 0 \), the graph shifts right; if

Which of the following equations is represented by the graph?
A. f(x) = |x+3| + 2
B. f(x) = |x+3| - 2
C. f(x) = |x-3| - 2
D. f(x) = |x-3| + 2

Explore how to match the correct absolute value equation to its graph by understanding horizontal and vertical shifts. This problem uses the formula f(x) = |x - h| + k, applying transformations and analyzing shifts. Ideal for students in Grades 8-10.

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