https://file.aiquickdraw.com/mathbot/file/17268438439832hl5bp8m.jpg

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


The graph provided shows a V-shaped curve, which is characteristic of an absolute value function. To determine the equation that represents the graph, we need to analyze a few key features:

1. **Vertex of the graph**: 
   The vertex of the V-shape appears to be at \( (-3, 2) \). This means the absolute value function has been shifted horizontally to the left by 3 units and vertically up by 2 units.

2. **Orientation and slope**: 
   The graph opens upwards, indicating a positive slope, and there are no reflections.

The general form of an absolute value function is \( f(x) = a|x-h| + k \), where:
- \( (h, k) \) is the vertex,
- \( a \) controls the steepness (which here seems to be 1 since the slopes on either side of the vertex rise at a 45-degree angle).

### Step-by-Step Analysis:

- The vertex is \( (-3, 2) \), so the equation must involve \( |x + 3| \) and a vertical shift by 2 units upwards.
- Thus, the correct equation is \( f(x) = |x + 3| + 2 \).

### Therefore, the correct answer is:

**A. \( f(x) = |x + 3| + 2 \)**

Would you like more details or have any other questions? 

Here are some related questions to deepen your understanding:
1. How would the equation change if the graph opened downwards?
2. What effect does changing the slope value \( a \) have on the graph?
3. How would you describe the graph of \( f(x) = |x - 3| - 2 \)?
4. What is the domain and range of the given absolute value function?
5. How would a vertical stretch affect the graph of \( f(x) \)?

**Tip**: The vertex form of an absolute value function \( f(x) = a|x-h| + k \) allows you to easily identify shifts and transformations of the graph.

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

Learn how to identify the correct equation for an absolute value function based on a graph. This problem covers absolute value functions, horizontal and vertical shifts, and graph transformations. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation