Question

For the function f(x)=-2sin(4x-pi), find the amplitude, period, phase shift, right end point, x and y axis orientation, and vertical shift.

Answer 1

This is what I have for:
Amplitude=-2
Period=pi/2
Phase Shift=pi/4
Right end point=3pi/4
X-axis: yes
Y-axis: No
Vertical Shift: None?

Answer 2

What does `right end point` mean? :o

Answer 3

Right End Point is the ending of the complete cycle. Formula I was give is c/b + 2pi/b. In other words, the (phase shift)+(period).

Answer 4

Ah oh ok ok ok :) End of one cycle, starting from x=0.
Ok good!
Looks great so far!

And what does `x-axis` mean? Symmetry?

Answer 5

X-axis orientation. In other words, is it reflected over the x-axis?

Answer 6

Same for Y-axis.

Answer 7

Oh oh I see, the negative tells you that it's reflected over the x-axis.
Ok good good good.

If you're listing the reflection separately, then you might want to list the amplitude as just the `magnitude` of the wave. Meaning drop the negative.
It's amplified by 2, the negative just tells us about reflection.

But you probably know your teacher better than I do, so I dunno :)

Answer 8

I guess I wanted to make sure my math was right for the period and right end point. And wasn't completely sure of the vertical shift.

Answer 9

Period is 2pi over B.
2pi divided by 4 simplifies to pi/2. good good good.

pi/4 + pi/2 = 3pi/4

yay!

Answer 10

She simply said that if \[a >0 then \it is \not reflected the x-axis. \]

Answer 11

Oops. If a>0, then it does not reflect over the x-axis. If a<0, it does.

Same concept for the y-axis only using b.

Answer 12

Oh ok c: then she wants you to include it in the amplitude, ok cool

Answer 13

So, for "Find the vertical shift", which I believe is represented by D, the answer would be none?

Answer 14

Your function,\[\Large\rm f(x)=-2\sin(4x-\pi)\]is actually this,\[\Large\rm f(x)=-2\sin(4x-\pi)+0\]So yes, no vertical shift. That sounds correct :)

Answer 15

Awesome! Thank you for the reassurance. End of the semester, could use all the correct answers possible.

Answer 16

heh :3