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Problem 8 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) $y=-2 \cos (x / 4)$
(b) $y=-2 \cos (\pi x / 4)$

Answer

(a.) amplitude $=2,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{1 / 4}=8 \pi$$x$ -intercepts $=2 \pi, 6 \pi$$x$ increases in $(0,4 \pi)$
(b.) amplitude $=2,$ period $=\frac{2 \pi}{\pi / 4}=8$$x$ -intercepts $=2,6$$x$ increases in (0,4)

Discussion

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Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Video Transcript

So for part A, we have why is equal to negative to co sign off X over four. So far thing is, was the attitude. The amplitude is true. Pete. Here is two pi divided by 1/4, and that's equal to it. So let's trot this graph here on the X axis. The points we would be interested in would be to pie for pie six pie and eight by and on the horizontal access we're interested in. We're Why's he going to two and we're wise equal to negative. So the range off the function is from negative to positive. Now let's draw this crap. This is a negative course and crabs with star check. Where was it into negative, too? And like this, this and now the X intercepts. So two X intercepts. The X is equal to two pi, and we have X is equal to 65 and the function is increasing over their excess equal to zero to where X is equal to four pipe. So that's party. Now let's talk about part B. So for part B, the equation is why is equal to negative to co sign off high ex score four. So the amplitude would still be, too. The PdF now is two pi invited by a coyote or four which will be able to eat. So let's try this. Points on the X axis we're interested in are 246 and eat. And on the X axis we're interested in on the Y axis. We're interested in bicycle to to advise equal to negative. So just trot his horizontal lines for guide. And now this is a negative close and Grasso starts at the bottom here and then goes up like this this and the doctor, not for the X intercepts. So there are two X intercepts which are a Texas equal to two and at X is equal to six. And then we also want to talk about where is the function increasing So we can see that it is increasing over where X is equal to 02 where X is equal to four

Other Schools
Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University