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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) $y=3 \sin (\pi x / 2)$(b) $y=-3 \sin (\pi x / 2)$

## (a.) amplitude $=3,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{\pi / 2}=4$(b.) amplitude $=3,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{\pi / 2}=4$

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##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

So here are the equations. So for part, Harry, why is equal to three sign Hi X over two and for part B B. Why is he called true? Negative three. Sign Hi X over two. So for both of those grafts, we would have similar information except for the craft. So let's start with the aptitude. So for both off them, he amplitude is equal to city. For both of them, the period would be to pie divided by pi over two and that he close four. So let's see if you could draw them. So on the X axis, we're interested in points where exit with 123 and four and then the, uh, why that has been interested in R C and negativity. So see graphs will not go off. Why is equal to three and they will not go below y is equal to negative. Okay, So since Saudi taxis are all set up, let's go ahead and draw the graph for a party. So the red line here is the one for parking. Now let's draw the graph for part B and for part B, they would be the same esta graph for party only reflected over the X axis because of that negative three. So here's what the graph of heart people look. So now, for both of them, we have to say X intercepts. So what are the X intercepts we have? X is equal to zero and then we have X is equal to two and then we have access. You cook too before now for the part. Where is each function increasing? So now for part A, we would say that the function is increasing over. Remember for me, that's the ready line, right? So from 0 to 1 and from sea to four and for part B, we're looking at the green nine. So we would say the dream line is increasing over from 1 to 3.

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##### Kristen K.

University of Michigan - Ann Arbor