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Problem 7 Medium Difficulty

Graph the functions for one period. In each case, specify the amplitude, period, $x$ -intercepts, and interval(s) on which the function is increasing.
(a) $y=\cos 2 \pi x$
(b) $y=-4 \cos 2 \pi x$

Answer

(a.) amplitude $=1,$ period $=\frac{2 \pi}{2 \pi}=1$$x$ -intercepts $=0.25,0.75$$x$ increases in (0.5,1)(b.) amplitude $=4,$ period $=2 \pi / 2 \pi=1$$\mathrm{x}$ -intercepts$=0.25,0.75$ncrenses in $(0.1 / 2)$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Video Transcript

So we have Ah, part A. For which it says Why is equal to co sign two pi X So the amplitude here would be one. The period would be two pi divided by two pipe which is equal to what? So in order to draw a graph, we are going to need points where X equals is your point to find your 0.0.5, you know, 0.75 and 1.0 and the aptitude is one. So we will just put these lines that why is it going to one and likewise equal to negative one? So these with service guy ignites. So we're now already control the graph and this is what the graph will look like. So the next thing you want to talk about our p X intercepts Okay, so there are two X intercepts at X is equal to 0.25 and it X is equal to 0.75 And then the function is increasing over X values going from 0.52 one place you. Now let's take a look at part B. So for part B, the equation we have is wife's equal to negative four co sign two pi X. So the aptitude is four. The P idiot is too high, divided by group. I just going to one. So let's draw this graph here on the X axis. Very interested in France where it is, we will point to 5.50 point 75 and one point you on the fly access we're interested in and where y is equal to four and where what is equal to negative for. So let's put these two horizontal lines in there now. We're already draw the graph. Since it's a negative course and function its star that Y is equal to negative for so this is worth the graft would look like so X intercepts. There are two X intercepts at X equal to 0.25 and X is equal to 7.75 and then the function is increasing over X values reading from 0 to 0.5

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College