Problem

What do all members of the family of linear funct…

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Problem 8 Medium Difficulty

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.

Name: what do all members of the family of linear functions fx 1 mx 3 have in common sketch several member
Uploaded: 2020-05-02
Duration: 1 min 22 s
Channel: Numerade
Description: 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.

Answer

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

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

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Video Transcript

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

Heather Z.

Oregon State University

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

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