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Let $ f $ and $ g $ be linear functions with equations $ f(x) = m_1 x + b_1 $ and and $ g(x) = m_2 x + b_2 $. Is $ f \circ g $ also a linear function? If so, what is the slope of its graph?

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02:06

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

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

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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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here we have two linear functions F N g, and we're going to find f of G and see if it's linear or not. So that means we're going to put the G function inside the F function and it will look like this m sub one times m sub two x plus B sub to plus B some to now let's simplify it and see if it looks like it's the equation of a line so we can distribute the EMS of one. And we have m sub one times m sub two times X plus m sub one times be siptu plus B sub to. So what I'm seeing here is I'm seeing some function. Why that has some number times X plus some other number. That, to me, looks like Why equals some slope times X plus some? Why intercept? So, yes, it's linear now because it's linear. We're supposed to say what the slope is. So this right here was the slope, the number that we multiplied by X So the slope is M one times m two

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