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Problem 6 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) $y=2 \sin \pi x$
(b) $y=-2 \sin \pi x$

Answer

(a.) amplitude $=2,$ period $=2$$x-$intercepts$=0,1,2$xincreasesin$(0,1 / 2),$ and $(3 / 2,2)$
(b.) amplitude$=2,$ period $=2$$x$ -intercepts $=0,1,2$$x$ increases in $(1 / 2,3 / 2)$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Heather Z.

Oregon State University

MG
Maria G.

Numerade Educator

Video Transcript

So we have Ah, part A. Which is why is equal to to sign my ex and part B says why is equal to negative two son by X. So these two graphs will be similar to each other as we and legs. So far, thing is, for both of them, the aptitude is to and for post office them, period is two pi divided by pi, which is equal to two, so both of them would have a period of two. So with that, we can ask you go ahead and draw those two graphs so points off interest on the X axis. What is your 20.5110 1.5 and two points. The aptitude is too. So let's set up our axes. So just to guide us export horizontal line that Y is equal to two and also advise it too negative too. So now let's draw the graph for wise equal to to sign Pi X. So the red line here is to sign Pikes Now for negative to sign pious. We just need to take this red car and reflected over the X axis. Okay, so there is our graph for Poppy So now the next thing we want to talk about for both off those graphs, they have the same X intercepts. So what are the X intercepts? The X intercepts are excess equal to zero, and X is equal to one and X is equal to two. And the last thing you want to talk about is where are those functions increasing? So, for party, we say it is increasing over exciting. It's going from zero to you don't 0.5 and also for X values going from 1.5 to 2.0. And for part B, we can see that the green curve is increasing for from X is equal to 25 to where X is equal to 1.5.

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Heather Z.

Oregon State University

MG
Maria G.

Numerade Educator