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# 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) $y=2 \sin x$(b) $y=-\sin 2 x$

## (a.) amplitude $=2,$ period $=2 \pi$$x -intercepts =0, \pi, 2 \pi$$\mathrm{x}$ increases in $(0, \pi / 2),$ and $(3 \pi / 2,2 \pi)$(b.) amplitude $=1,$ period $=2 \pi$$\mathrm{x} -intercepts =0, \pi, 2 \pi$$x$ increases in $(\pi / 2,3 \pi / 2)$

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So for part game we're gonna talk about by is equal to it's to sign ICS. So for thing is theon pick it is too and the P it is two pi. So let's draw the graph first. So we have a pie or two. Hi. Setting up the axis cream pie or two and then to buy the amplitude is too. So the why values will not go above two and they will not cope. It'll negative. So before we start trying the craft that sister FT ACSI set up now we're ready to draw the graph. So this is what the graph, But like so amplitude as we said earlier, is he called to to the PD. It is equal to two pi. The X intercepts that are three X intercepts at X is equal to zero at X is equal to pi, and that X is equal to two pi and then it's increasing over two intervals. So the intel so which light is increasing, are from zero too high over to on and from three pi over two too high to two pi. So that's a part a. Now let's talk about part B. So for part B or we have Why is equal to negative Sign two x So the articulate is gonna be one and the pdf, which is two pi divided by two for people to pie. So let's see, You can draw this graph So our point of interest would be Tyra for parts were too. Did he pi over four and pie and then, since the amplitude is one so the graph will be limited between a positive one and negative, so the values won't go outside of these blue lines. Now it's a negative sign graph, so it doesn't start by going up from the origin started by going down to rich from the origin. So there is the graph. Now that we have to graft, we can talk about the X intercepts. So what are the X intercepts? There are three X intercepts. X is equal to zero. X is equal to pi over two, and X is equal to high. And then we also want to talk about the interval. Always T function is increasing, so it is increasing over pile of four true two D piro before

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