Question

What are the amplitude, period, phase shift, and midline of f(x) = -3 sin(4x - π) + 2? (5 points)

Answer 1

@Owlcoffee

Answer 2

http://gyazo.com/79c729685b340c46e3861aac421894b3

Answer 3

what do you think the amp is?

Answer 4

that is all you really have to know to get this question

Answer 5

how do i find it

Answer 6

oh I thought you would know how because it is the easiest thing to find
it is the absolute value of the constant number being multiplied to the trig function there

Answer 7

so 3?

Answer 8

yep

Answer 9

you are done because there is only one option with amp=3

Answer 10

lol yay thanks

Answer 11

http://gyazo.com/0060f7a559b9d1fb6d4bef7b957a2c03 is that answer right

Answer 12

in any trigonometric equality with the form:
\[y=Asin(ax+ \alpha) \]
The amplitude is the number "A" and you can calculate the period with:
\[p=\frac{ 2 \pi }{ a }\]

Answer 13

you mean the amp=|A|?

Answer 14

\[y=A \sin(bx+c)+d \\ \text{ amp } =|A| \\ \text{ period } =\frac{2 \pi}{|b|} \\ \\ \text{ phase shift : } \text{ solve for } x : bx+c=0 \\ \text{ max if } A \text{ is } \text{ positive is } A(1)+d=A+d \\ \text{ min if } A \text{ is } \text{ positive is } A(-1)+d=-A+d \\ \text{ so the average the of max and min is }=\frac{(A+d)+(-A+d)}{2}=\frac{2d}{2}=d \\ \text{ the midline is therefore } y=d\]

Answer 15

thank you for all of that

Answer 16

was my answer correct for the other 1?

Answer 17

oh yep you can apply the same information I just gave to that one
you have period is 2pi
2pi=2pi/|b|
means |b|=1
which means b=-1 or b=1
phase shift (think horizontal shift): solve inside=0 to get phase shift
and as you see x-pi=0 gives x=pi
so pi is the phase shift
the vertical shift is yes the number hanging outside the d=-4

Answer 18

yay thank you :)