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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 = \sin (\frac{1}{2} x) $

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01:38

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

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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.

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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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to graph this function, we're going to start by looking at the graph of the standard function y equals sign of X, so we know that it has a period of two pi. That's the with that one cycle, and we knew it goes up to a height of one and down to a height of negative one. So it looks roughly like this. Now what happens to it if we multiply the X by 1/2 that represents a horizontal stretch, so it's going to be two times as wide. So we say horizontal stretch by a factor of two that changes the period. The width of one cycle is now going to be four pi instead of two pi. So if you want to draw it out that far, we can still goes up to a height of one and down to a height of negative one. That didn't change. So now we have the graph that is stretched out wider, like so

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