Question

HELP!! w/ graphing....

y= -2-2cosPix Trying to figure out x-intercepts?, or how am i supposed to shift?

Answer 1

So we want to set this equal to 0 and see what we can get:

0 = \(-2-2cos(\pi\ x)\)

After simplifying you get:
\[-1 = \cos( \pi x)\]

So to solve this, I want to forget about that pi for now. Where would cos(x) be equal to -1?

Answer 2

cos x would be equal to -1 @ pi

Answer 3

oh my gosh i'm sorry, i miswrote the original problem , it's y= -2-2 cos 3pi x

Answer 4

Right. So that means the angle inside of cos(x) needs to be pi if Im going to get -1. So if I want that to happen, i need to solve:
\[3\pi x = \pi + 2k \pi\] The 2kpi is because the period of cosine is 2pi, and we dont have an interval, so we're assuming this carries on forever.

Missing the 3 in there doesnt affect any of the previous steps, so I didnt have to delete anything thankfully, lol.

Answer 5

i;m not sure how i would solve for 3pix = pi + 2kpi?

Answer 6

Well, we want to get x by itself. So I would be dividing both sides by 3pi
\[x = \frac{ 1 }{ 3 }+\frac{ 2k }{ 3 }\]

So all x-intercepts will be at 1/3 plus or minus any integer multiple of 2/3.

Answer 7

ok. I see what your saying.

Answer 8

If k = -3, x-int = -5/3
if k = -2, x-int = -3/3
if k = -1, x-int = -1/3
if k = 0, x-int = 1/3
and this can continue on forever, just each x-intercept would be 2/3 distance away

Answer 9

So since this particular graph is reflected across the x-axis, how come the amplitude is 2 when -2-2 equals -4?

Answer 10

The amplitude is the absolute value of the number multplying your trig function. So yes, you have -2-2cos(3pix), but the number multiplying cos(3pix) is -2 and only -2. This makes the amplitude 2.

Answer 11

so on the graph, the first point I graphed is at 0,-4 but why wouldn't the graph be at 0,-2 then go up to positive 2?

Answer 12

So in general:



The idea is that your first point, x = 0, is going to be at the highest point of cosx or the lowest point of cosx. Since we have cosx to be negative in your problem, that (0,-4) point is a minimum value.

The amplitude is measured from the middle line of the graph.



The idea is that youre at a minimum value. Because you have an amplitude of 2, you can only increase by a maximum of 4. So the highest y-value you will ever have is y= 0