Question

What is a possible formula for the graph attached inside?

f(x)=__________

please explain! Thank you :)

Answer 1

graph! :)

Answer 2

Looks like a sin that has been moved up 6, has an amplitude of 3 and period of 14 pi

Answer 3

ohh so does it follow the format of f(x)=AsinBt?

Answer 4

It's a sine curve, going to be something like

f(x) = AsinBt + C

Answer 5

might be easier to think of it as a cosine with a horizontal displacement of -7pi/2

Answer 6

oh... so right now it would look something like this?

f(x)=3sin(14pi)(6)+C

? or did i not substitute them right? :/

Answer 7

what do you mean by the horizontal displacement?

and would it be like f(x)=AcosBt if you do it that way? :/

Answer 8

f(x) = AsinBt + C

where A is negative, will give that shape

Answer 9

so if the amplitude here is 3, the A in the equation is -3?

Answer 10

Yes

Answer 11

okay, so now it's like this?

f(x)= -3sinBt+C ?

Answer 12

to find B, you can't just plug in 14pi.

B = 2pi/T where T is period

B = 2pi/14pi

Answer 13

oh so do you simplify that to 1/7 ? or do you have to leave it like 2π/14π ?

Answer 14

Always simplify everything, is pretty safe to do

Answer 15

oh okie :)

so now we're at f(x)= -3sin(1/7)(14pi) + C ?

did i get that right? :/

Answer 16

t is still t, the variable (notice you don't have a variable)

f(x) = AsinBt + C

A is the amplitude, -3, B is 1/7, C is how much it's shifted up, 6

Answer 17

ohh so it becomes

f(x)= -3sin(1/7)t + 6
?? if that's right (which i'm hoping i plugged in correctly this time lol) do you simplify any more?

Answer 18

Nope, that looks about right.

Answer 19

But writing it as f(x)= -3sin(t/7) + 6 is prob easier

Answer 20

ahh okay awesome!! thank you!!! :)