https://file.aiquickdraw.com/mathbot/file/17273622722560e4sou5b.jpg

The image contains several mathematical problems related to absolute value functions and a question regarding fishing depth based on a given formula.

Here’s a breakdown of the problems from the image:

### 1. **Identifying the Absolute Value Function Graph**
   The first problem asks to identify the graph of the absolute value function:
   
   \[
   y = |x + 5| + 2
   \]
   
   To solve this:
   - The general form of an absolute value function is \( y = |x - h| + k \), where \( (h, k) \) is the vertex of the graph.
   - For \( y = |x + 5| + 2 \), the vertex is at \( (-5, 2) \), and the graph opens upwards.

   The correct graph should show a V-shape with the vertex at \( (-5, 2) \).

### 2. **Matching the Equation to a Graph**
   In the second part of the image, you are asked to find the equation of the absolute value function corresponding to the given graph (E).

   You can determine the equation by identifying:
   - The vertex of the graph.
   - The slope of the lines on each side of the vertex.
   
### 3. **Fishing Depth Question**
   The third question gives a function for maximum depth:
   
   \[
   f(x) = 6|s - 237| - 432
   \]
   
   You are asked to determine the range of depths based on the conditions provided. This involves solving for \( s \) when the value of \( f(x) \) lies between two given bounds.

---

Do you want detailed step-by-step solutions for each question? Here are 5 related questions that can expand on these topics:

1. How do you find the vertex of an absolute value function?
2. How does the transformation of an absolute value function affect its graph?
3. What is the general approach to match an equation to a graph of a piecewise function?
4. How can you solve absolute value equations algebraically?
5. What is the method to solve real-life problems using absolute value functions?

**Tip:** Absolute value graphs are always V-shaped, and their vertex can easily be identified by setting the expression inside the absolute value equal to zero.

The image contains several mathematical problems related to absolute value functions and a question regarding fishing depth based on a given formula.

Explore how to graph absolute value functions and solve real-world problems, including graph transformations and determining fishing depths based on the formula f(x) = 6|s - 237| - 432. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation