Question

What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1?

Answer 1

f(x) = −1 cos πx + 2

f(x) = −1 cos (x − π) + 2

f(x) = 2 cos (x − π) − 1

f(x) = 2 cos πx − 1

Answer 2

@ash2326

Answer 3

\[y=a\cos (bx-c)+d=a\cos\left(b\left(x-\frac{c}{b}\right)\right)+d\]
\(|a|\) is the amplitude, \(\dfrac{2\pi}{b}\) is the period, \(\dfrac{c}{b}\) is the horizontal shift, and \(d\) is the vertical shift.

Answer 4

You're given that \(|a|=2\), which means \(a=2\) or \(a=-2\). You can eliminate the first two choices.

Answer 5

The period is \(2\pi\), which means
\[\frac{2\pi}{b}=2\pi~~\iff~~b=1\]
So you can eliminate the fourth choice.

Answer 6

omg thank you, can you explain the rest please?

Answer 7

Also, can you help me a few more? Trig- is not my strongest subject

Answer 8

@SithsAndGiggles

Answer 9

Explain the rest? What else is there to explain?

Answer 10

you explain how to find the amplitude and the period

Answer 11

how do find the horizontal and vertical shifts

Answer 12

?

Answer 13

Okay, so \(d\) is pretty easy to identify. The vertical shift is -1 (or 1 unit down), so \(d=-1\).

Answer 14

You have a horizontal shift of \(\pi\), so
\[\frac{c}{b}=\pi\]
We figured out that \(b=1\), so \(c=\pi\).

Answer 15

Thank you. You're amazing. Can you help me with another?

Answer 16

Sure, but post it as a different question. I might not respond in a timely fashion, I'm a bit busy here, so someone else may be able to assist you.

Answer 17

Ok, can I still tag your name?

Answer 18

I'm closing the question :)

Answer 19

Wait so what one is it?