Math Problem Statement

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

Solution

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∣+kf(x) = |x - h| + k

Where:

  • hh represents a horizontal shift: if h>0h > 0, the graph shifts right; if

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Math Problem Analysis

Mathematical Concepts

Absolute Value Functions
Graph Transformations

Formulas

f(x) = |x - h| + k

Theorems

Translation Theorem for Absolute Value Functions

Suitable Grade Level

Grades 8-10

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