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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^2 - 4x + 5 $

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01:39

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

Idaho State University

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.

06:41

Graph the function by hand…

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our goal is to graft dysfunction, but we want to do it by thinking about the parent function, which is y equals X squared and what kinds of transformations would have taken place. So we need to change how this function looks before we can figure that out. So what I'm going to do is complete this square and I have y equals X squared minus four X plus four. That's a perfect try. No meal square plus one. So I just broke up the plus five into plus Foreign plus one. Now we can write the perfect try no meal square as X minus two quantity squared. So looking at this graph, this would be the original function y equals X squared, shifted to the right one, rescued me right to and shifted up one. Okay, so let's take a look at the regular graph of y equals X squared. Just it's for Texas 00 problem opening up. So now if we shift that to the right to and up one, we get something like this

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