Use transformation, showing all work. Use interval notation. Problem attached **Graphing Transformed Functions**In this activity, we will use transformations to graph the function and state the domain and range using interval notation.The function we will be working with is:\[ y = -\sqrt{x + 2} + 1 \]**Steps and Transformations:**1. **Base Function:** - The basic function here is $ y = -\sqrt{x} $, which is a reflection of the square root function $ y = \sqrt{x} $ across the x-axis.2. **Horizontal Shift:** - The expression $ x + 2 $ indicates a horizontal shift to the left by 2 units. This transformation moves the graph of $ y = -\sqrt{x + 2} $.3. **Vertical Shift:** - The addition of $ +1 $ at the end of the function raises the graph vertically by 1 unit. So, we get $ y = -\sqrt{x + 2} + 1 $.Using the transformations, we sketch the graph as follows:**Graphs and Diagrams Explanation:**- The coordinate plane is labeled with both x and y axes ranging from -5 to 5.- The graph starts at $ (-2, 1) $ since at $ x = -2 $, $ \sqrt{0} = 0 $ and $ y = 1 $.- As $ x $ increases, the function $ y = -\sqrt{x + 2} + 1 $ decreases because of the negative sign before the square root, reflecting the curve downward.**Domain and Range:**- The **domain** is the set of all x-values that can be input into the function. Since the inside of the square root $ x + 2 $ must be non-negative, the domain is: \[ x \ge -2 \quad \text{or in interval notation:} \quad [-2, \infty) \]- The **range** is the set of all possible y-values of the function. Given the transformations applied: - The highest point on the graph is at $ y = 1 $. - As $ x $ increases, $ y $ will continue to decrease indefinitely. Hence, the range is: \[ y \le 1 \quad \text{or in interval notation:} \quad (-

We have to find the domain and range of the function also graph the function.…

Answered: Use transformations to graph the…

Use transformations to graph the function and state the domain and range using interval notation. y = -√√x+2+1 1+ -4 4 -2 -1

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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Question

Use transformation, showing all work. Use interval notation. Problem attached

**Graphing Transformed Functions**

In this activity, we will use transformations to graph the function and state the domain and range using interval notation.

The function we will be working with is:

\[ y = -\sqrt{x + 2} + 1 \]

**Steps and Transformations:**

1. **Base Function:**
- The basic function here is $ y = -\sqrt{x} $, which is a reflection of the square root function $ y = \sqrt{x} $ across the x-axis.

2. **Horizontal Shift:**
- The expression $ x + 2 $ indicates a horizontal shift to the left by 2 units. This transformation moves the graph of $ y = -\sqrt{x + 2} $.

3. **Vertical Shift:**
- The addition of $ +1 $ at the end of the function raises the graph vertically by 1 unit. So, we get $ y = -\sqrt{x + 2} + 1 $.

Using the transformations, we sketch the graph as follows:

**Graphs and Diagrams Explanation:**

- The coordinate plane is labeled with both x and y axes ranging from -5 to 5.
- The graph starts at $ (-2, 1) $ since at $ x = -2 $, $ \sqrt{0} = 0 $ and $ y = 1 $.
- As $ x $ increases, the function $ y = -\sqrt{x + 2} + 1 $ decreases because of the negative sign before the square root, reflecting the curve downward.

**Domain and Range:**

- The **domain** is the set of all x-values that can be input into the function. Since the inside of the square root $ x + 2 $ must be non-negative, the domain is:
\[
x \ge -2 \quad \text{or in interval notation:} \quad [-2, \infty)
\]

- The **range** is the set of all possible y-values of the function. Given the transformations applied:
- The highest point on the graph is at $ y = 1 $.
- As $ x $ increases, $ y $ will continue to decrease indefinitely. Hence, the range is:
\[
y \le 1 \quad \text{or in interval notation:} \quad (-

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