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The graph of $ y = \sqrt{3x - x^2} $ is given. Use transformations to create a function whose graph is as shown.

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03:03

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Campbell University

Oregon State University

University of Nottingham

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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The graph of $ y = \sqrt{3…

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The graph of $y=\sqrt{3 x-…

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Graph the function using t…

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Okay, let's figure out what happened to change one graph to the other. What kinds of transformations? And then we can make changes to the equation. So noticed that the width of the original graph has not changed. It was three units wide, and it's still three units wide. However it hit it, hit it has shifted right? Two units also noticed that the height has changed. It was originally 1.5 units tall, and now it's three units tall. So that would be a vertical stretch. Times two by a factor of two. Okay, so to reflect that in the equation, the vertical stretch is going to be multiplying by two on the outside. And then the shift right to is going to be subtracting two from X and notice that we have X in two places. So we have to subtract two from each X, and that will be the equation of what we just have seen drawn

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