What is the graph? Domain & Range? please help?? **Graph the Function Using Transformations**Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.\[ h(x) = \sqrt{x} + 2 \] The image displays a graph of the function $ y = \sqrt{x} $. Below is a detailed explanation:### Description of the Graph:- **Axes**: The graph is plotted on a Cartesian plane with the horizontal axis labeled as $ x $ and the vertical axis labeled as $ y $. Both axes range from $-12$ to $12$.- **Curve**: The function $ y = \sqrt{x} $ is depicted as a curve starting at the origin (0,0) and extending towards the right. The curve is only defined for non-negative values of $ x $ (i.e., $ x \geq 0 $) since the square root of a negative number is not a real number.- **Direction**: The curve rises slowly as it moves to the right, indicating that as $ x $ increases, $ y $ (i.e., $ \sqrt{x} $) also increases, but at a decreasing rate.- **Key Points**: No specific key points are marked on the graph, but it is clear that the curve passes through the origin.### Characteristics of the Function:- **Domain**: $ x \geq 0 $- **Range**: $ y \geq 0 $- **Intercept**: The graph intersects the origin (0,0).This graphical representation is useful for visualizing how the square root function behaves, illustrating its increasing nature and showing its restriction to non-negative values of $ x $.

To graph a function f(x+a), shift the graph of f(x) a units to the left. Therefore, to draw the…

Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.

Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

What is the graph? Domain & Range? please help??

**Graph the Function Using Transformations**

Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.

\[ h(x) = \sqrt{x} + 2 \]

The image displays a graph of the function $ y = \sqrt{x} $. Below is a detailed explanation:

### Description of the Graph:

- **Axes**: The graph is plotted on a Cartesian plane with the horizontal axis labeled as $ x $ and the vertical axis labeled as $ y $. Both axes range from $-12$ to $12$.

- **Curve**: The function $ y = \sqrt{x} $ is depicted as a curve starting at the origin (0,0) and extending towards the right. The curve is only defined for non-negative values of $ x $ (i.e., $ x \geq 0 $) since the square root of a negative number is not a real number.

- **Direction**: The curve rises slowly as it moves to the right, indicating that as $ x $ increases, $ y $ (i.e., $ \sqrt{x} $) also increases, but at a decreasing rate.

- **Key Points**: No specific key points are marked on the graph, but it is clear that the curve passes through the origin.

### Characteristics of the Function:

- **Domain**: $ x \geq 0 $
- **Range**: $ y \geq 0 $
- **Intercept**: The graph intersects the origin (0,0).

This graphical representation is useful for visualizing how the square root function behaves, illustrating its increasing nature and showing its restriction to non-negative values of $ x $.

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