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(a) How is the graph of $ y = 2 \sin x $ related to the graph of $ y = \sin x $? Use your answer and Figure 6 to sketch the graph of $ y = 2 \sin x $.

(b) How is the graph of $ y = 1 + \sqrt{x} $ related to the graph of $ y = \sqrt {x} $? Use your answer and Figure 4(a) to sketch the graph of $ y = 1 + \sqrt{x} $.

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02:57

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

Johns Hopkins University

Missouri State University

Harvey Mudd College

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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Sketch the graph of the eq…

Okay, First of all, let's take a look at the graph of y equals sign of X. So why it will sign of X goes through these points. Here's a sign curve, and that continues. They're infinitely many of them. Well, just draw some of it. Okay, So what happens if you multiply that by two? That would be a vertical stretch. So it's going to be two times is tall. So notice that the regular Siggraph goes up to a height of one and down to a height of negative one. So this new graph is going to go up to a height of two and down to a height of negative, too. We say that the amplitude has changed. We call it amplitude when we're talking about a sign graph. All right, so there's the graph. Two times is tall. Any we go on and on infinitely far to the right and left as well. Now, for part B, what about the graph of y equals square root? X. So that goes through the 0.114 to here's what the square root graft looks like. What happens if we had one to it? We shift the whole Graf up one. So the point that was at 00 is going to be at 01 The point that was at 11 is going to be at 12 And the point that was at 42 is now going to be out for three. So looks the same, but just shifted up one.

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