## Function Analysis and Contour MapsConsider the function $ f(x, y) = \sqrt{x^2 y} $.### Task a: Domain of $ g $We need to sketch or describe the domain of the function $ g $.The domain is given by:\[ \text{Domain} = \{ (x, y) \mid y \geq 0 \} \]This means the function is defined for all values of $ x $ and $ y $ where $ y $ is greater than or equal to zero.### Task b: Contour MapYou are asked to sketch a contour map (level curves on one set of axes) for $ z = 1, 2, 3 $. To visualize this, you can use the following link to an online graphing tool:[Desmos Calculator](https://www.desmos.com/calculator/lqsz6yuywz)The contour map will represent the level curves of the function for different values of $ z $. For each $ z $, the contour represents the set of points $(x, y)$ where $ f(x, y) = z $.By inputting the function into the graphing tool, you can explore the level curves for specific values of $ z $ such as 1, 2, and 3. This aids in understanding how the function behaves and the shape of the contours in its domain.

Answered: Image /qna-images/answer/2637eb11-4a57-4a59-9e81-b5662230cbaa.jpg

Answered: Let f(x.y) = ry. a. Sketch/describe the…

Let f(x.y) = ry. a. Sketch/describe the domain of g Domain = { (x,y)]yz0} b. Sketch a contour map (level curves on one set of axes) for z = 1,2,3. https://www.desmos.com/calculator/lqszáyuywz

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

## Function Analysis and Contour Maps

Consider the function $ f(x, y) = \sqrt{x^2 y} $.

### Task a: Domain of $ g $
We need to sketch or describe the domain of the function $ g $.

The domain is given by:
\[ \text{Domain} = \{ (x, y) \mid y \geq 0 \} \]

This means the function is defined for all values of $ x $ and $ y $ where $ y $ is greater than or equal to zero.

### Task b: Contour Map
You are asked to sketch a contour map (level curves on one set of axes) for $ z = 1, 2, 3 $.

To visualize this, you can use the following link to an online graphing tool:
[Desmos Calculator](https://www.desmos.com/calculator/lqsz6yuywz)

The contour map will represent the level curves of the function for different values of $ z $. For each $ z $, the contour represents the set of points $(x, y)$ where $ f(x, y) = z $.

By inputting the function into the graphing tool, you can explore the level curves for specific values of $ z $ such as 1, 2, and 3. This aids in understanding how the function behaves and the shape of the contours in its domain.

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