I need step by step instructions on HOW to solve this pictured question. **Instruction to Solve the Problem: Finding the Vertex and Range of the Function****Problem:** What is the vertex and range of \( y = |x + 3| + 2 \)?**Solution:**1. **Identify the Function Type:** - The function is an absolute value function, which has the general form \( y = |x - h| + k \).2. **Determine the Vertex:** - In the function \( y = |x + 3| + 2 \), rewrite it in the form \( y = |x - (-3)| + 2 \) to identify \( h \) and \( k \). - The vertex of the function is at \( (h, k) = (-3, 2) \).3. **Find the Range:** - The standard form \( y = |x - h| + k \) indicates that the vertex is the minimum value point for the function, provided the coefficient of the absolute value is positive. - In this case, the minimum value of \( y \) is 2, when \( x = -3 \). - Since the vertex is the lowest point on the graph of \( y = |x + 3| + 2 \), the range is \( y \geq 2 \).**Summary:**- **Vertex:** \((-3, 2)\)- **Range:** \(y \geq 2\)

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I need the step by step instructions to solve the question What is the vertex and range of y = |x +31 + 2?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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I need step by step instructions on HOW to solve this pictured question.

**Instruction to Solve the Problem: Finding the Vertex and Range of the Function**

**Problem:**

What is the vertex and range of \( y = |x + 3| + 2 \)?

**Solution:**

1. **Identify the Function Type:**
- The function is an absolute value function, which has the general form \( y = |x - h| + k \).

2. **Determine the Vertex:**
- In the function \( y = |x + 3| + 2 \), rewrite it in the form \( y = |x - (-3)| + 2 \) to identify \( h \) and \( k \).
- The vertex of the function is at \( (h, k) = (-3, 2) \).

3. **Find the Range:**
- The standard form \( y = |x - h| + k \) indicates that the vertex is the minimum value point for the function, provided the coefficient of the absolute value is positive.
- In this case, the minimum value of \( y \) is 2, when \( x = -3 \).
- Since the vertex is the lowest point on the graph of \( y = |x + 3| + 2 \), the range is \( y \geq 2 \).

**Summary:**

- **Vertex:** \((-3, 2)\)
- **Range:** \(y \geq 2\)

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