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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.

All the members of this family are linear functions which represent straight lines passing through $(-3,1)$

01:47

Jeffrey P.

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

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Idaho State University

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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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