Question

What are the amplitude, period, phase shift, and midline of f(x) = 7 cos(2x + π) − 3?

Answer 1

Amplitude = −3; period: π; phase shift: x = negative pi over 2; midline: y = 3

Amplitude: 7; period: π; phase shift: x = negative pi over 2; midline: y = −3

Amplitude: 7; period: 2π; phase shift: x = pi over 2; midline: y = 3

Amplitude: −3; period: 2π; phase shift: x = pi over 2; midline: y = −3

Answer 2

If f(x) = Acos(Bx + C) + D, then:
Amplitude = A
Period = (2*pi) / B
Phase shift = -C / B
Midline is: y = D

Answer 3

Okay, so would I use that formula for all of them?

Answer 4

Yes. And the same formula applies if it is sine function instead of cosine.

Answer 5

okay I'll see what I get then let you know

Answer 6

Alright.

Answer 7

how do i find x?

Answer 8

Not sure what you mean? For this problem you don't have to solve for x.

Answer 9

But like in the formula thing there's x...

Answer 10

You probably think i'm really stupid ehhh sorry :(

Answer 11

You just compare the given function to the general function and identify the constants A, B, C and D and then plug it into the formula:
f(x) = 7 cos(2x + π) − 3 Compare this to the general form,
f(x) = Acos(Bx + C) + D
A = 7
B = 2
C = π
D = -3

Amplitude = A = 7
Period = 2π / B = 2π / 2 = π
....

Answer 12

OHHH okay thank you so muchhhh sorry for burdening you with all of my math problems I seriously do appreciate it :)

Answer 13

C is the correct answer right?

Answer 14

Hey, no problem at all. We are here to assist.

Not C. C has a period of 2π. We calculated the period above to be π.

Amplitude = A = 7
Period = 2π / B = 2π / 2 = π
To finish the other two:
Phase shift = -C / B = -π / 2
Midline is: y = D; y = -3

Answer 15

Okay. It's A?

Answer 16

?!

Answer 17

The answer we got above is:
Amplitude: 7; period: π; phase shift: x = -π / 2; midline: y = −3

Answer 18

Choice B.

Answer 19

I LOVE YOU

Answer 20

lol