💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = \mid \cos \pi x \mid $

See step for solution

01:58

Jeffrey P.

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

Campbell University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

01:59

Graph the function by hand…

01:00

02:37

02:38

04:50

02:34

01:17

00:39

04:42

01:27

to graph dysfunction. Let's start by thinking about the standard function Y equals co sign of X. What does that look like? Goes upto one down to negative one. It has a period of two pi. So the coast and graph in general looks like this. The regular standard Cho sang graph. Okay. And it keeps going forever to the left and the right. That's just part of it. Now what happens if we multiply the X pipe? I What does that do that's going to be a horizontal shrink by a factor of pie? That means it's pi times narrower than it used to be roughly three times narrower. So the period, the width of one cycle used to be two pi. Now the period is going to be just too. We divide the period by the horizontal shrink factor, so the period is just going to be, too. That's roughly three times narrower. Now, I'm not gonna make that perfectly to scale compared to the previous one. I'm just going to put a to here and a negative to here. We still go upto one down to negative one. That didn't change. So roughly here is the graph we have now. But now the final thing we want to do is the absolute value signs. So the absolute value is going to make it positive. Anything that was previously positive will still be positive. Anything that was negative is going to now be reflected across the X axis and made positive. Okay, so I graft was positive for a while. Then it went negative. So that negative part is going to be reflected back up. And it was positive for a while, and then it went negative and that negative parts going to be reflected back up. And then it was positive for a while, So that's what we get.

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Graph the function by hand, not by plotting points, but by starting with the…