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What do all members of the family of linear functions $ f(x) = 1 + m(x + 3) $ have in common? Sketch several members of the family.
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01:47
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 2
Mathematical Models: A Catalog of Essential Functions
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Missouri State University
Harvey Mudd College
Idaho State 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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When I look at this function, it reminds me of point Slope form, which is why minus y one equals m times X minus X one. And we use point slope form when we know the slope and when we know a point on the line. So what if we take the equation, were given and rearrange it a little bit so that it looks more like point slope form so we could subtract one from both sides and we have f of X minus one equals M Times X plus three. We could even replace f of X with y. So we have y minus one and we could replace X Plus three with X minus negative three. So this looks like a line with a slope of em that goes through the point Negative 31 All right, so these would be all the lines that go through the point. Negative. 31 Let's sketch several of them, so we have a point. Negative 31 And now let's sketch several points through that several lines. Through that point, this could be one. This could be one another one here, etcetera. Infinitely many options
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