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Define $f : \mathbb{R} \rightarrow \mathbb{R}$ by $f(x)=m x+b$a. Show that $f$ is a linear transformation when $b=0$ .b. Find a property of a linear transformation that is violated when $b \neq 0$ .c. Why is $f$ called a linear function?

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 8

Introduction to Linear Transformations

Introduction to Matrices

Campbell University

Oregon State University

McMaster University

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this question wants to know if f of X equals X plus two divided by two is a linear function. Well, it is. All we have to do is we're gonna separate this too, for both of this exodus to appear. So it'll look like f of X equals X over two plus two over too. So this is a safety guest saying X over to us in the ass, saying 1/2 X and then two divided by two is just one. So we can see now that this is in the form of Y equals in X plus B or 1/2 is our slope and one is our y intercept. So, yes, this is a linear function.

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