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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 = (x - 3)^2 $

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01:02

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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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 list. A graph y equals the quantity X minus three squared, and that's a transformation of the standard function y equals X squared. So let's start by picturing that standard function. It's a parable A with the vertex of 00 and it opens up. So what we want to do to get this function is to shift it to the right to write three. Excuse me. Okay, so what's that going to look like? Instead of having a Vertex at 00? It's going to have a Vertex at 30 and we could find the Y intercept by plugging in. Zero for acts will get nine. So way up there at nine. Wherever that is, we're going to have our Y intercept.

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