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

1. anonymous

@Owlcoffee

2. anonymous
3. freckles

what do you think the amp is?

4. freckles

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

5. anonymous

how do i find it

6. freckles

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

7. anonymous

so 3?

8. freckles

yep

9. freckles

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

10. anonymous

lol yay thanks

11. anonymous

12. Owlcoffee

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

13. freckles

you mean the amp=|A|?

14. freckles

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

15. anonymous

thank you for all of that

16. anonymous

was my answer correct for the other 1?

17. freckles

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

18. anonymous

yay thank you :)