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Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = 2 \sqrt{x + 1} $

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01:32

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

Campbell University

Harvey Mudd College

Baylor University

Lectures

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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.

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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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Graph the function by hand…

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Our goal is to graph y equals two times the square root of X plus one. But let's start with y equals square root X one of our standard functions. So let's remember what that looks like. We have this basic shape. It goes through 0011 for two, etcetera. Now what would it look like if I changed it to Why equals the square root of X plus one? That transformation would be a shift left one. So then we would have a point where the Vertex was at 00 Now it's going to be over here at negative 10 So it looks like that now what happens if I multiply that by two? That's going to be a vertical stretch by a factor of two, twice as tall. So what does that look like? Okay, so the point that was at negative 10 just a moment ago is still going to be at negative 10 Now, remember, Originally there was a 0.11 and that moved over 201 Well, now that's going to be twice as tall. So that's going to be at zero to. So we should did it left one, and we stretched it vertically twice. His talk

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