Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

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

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.

12:15

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.

02:25

What do all members of the…

01:14

01:24

00:50

01:21

03:25

01:15

0:00

Use the methods of this se…

00:41

? Families of Lines Use a …

00:46

00:51

01:11

Under what conditions is t…

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

View More Answers From This Book

Find Another Textbook