Question

What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?

Answer 1

amplitude is the number in front, aka 4
the period is how much time it takes for one revolution, u can graph this if u wanna, the phase shift is i think how much up and down? that would be how much you shift the function up and down

Answer 2

@AZ ? i cant really think rn

Answer 3

well i just know it's either the first or second too

Answer 4

forgot the negative, my bad for the amplitude but pretty sure amplitude always positive

Answer 5

yea im being dumb phase shift isnt up or down, wait for AZ

Answer 6

lol

Answer 7

y = A sin(B(x + C)) + D

A is our amplitude
\(\text{period} = \dfrac{2\pi}{B}\)
phase shift is C. If it's +C then it's going to the left. If it's -C then it's going to the right
D is our vertical shift

Answer 8

So which one is it, like, how is the period and phase shift determined then

Answer 9

okay then soooo, explain how to do it please?

Answer 10

y = A sin(B(x + C)) + D is what I had written

The equation they gave you is like this
\( y = A \sin(Bx + BC) + D\)

\(f(x) = -4(\sin(2x + \pi)) - 5\)

So first, let's factor out the 2 from \(2x + \pi\)
so we can find the phase shift and period

Answer 11

hmm but amplitude is how far from the center,
sorry if im being dumb xD

Answer 12

so.... AZ how do i figure out phase shift and period

Answer 13

can i guess the second one

Answer 14

I think you're right, darkknight. Amplitude should be the positive value regardless :)

Answer 15

okay, i kinda need to turn this in soon, could you please explainnnnnnn what the answer is pleaseee

Answer 16

f(x) = A sin (B(x + C)) + D

f(x) = -4 sin (2x + π) - 5

then take 2 from (2x + π)

f(x) = -4 sin 2(x + π/2) - 5

A = 4 ,

B = 2

C = π/2

D = -5

A = the amplitude

Amplitude = -4

Period = 2π/B

The period = 2π/2 = π

C is the phase shift

The phase shift π/2 to the left

Amplitude = -4

period = π

phase shift: x = π/2

SO

Amplitude = -4; period = π; phase shift: x = π/2 is your answer

Answer 17

LOL I had forgotten to post

Answer 18

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
so.... AZ how do i figure out phase shift and period
\(\color{#0cbb34}{\text{End of Quote}}\)

So

we have
\(2x + \pi\)

Let's factor out 2, what do we get?
\( 2(x + \dfrac{\pi}{2})\)

Answer 19

Now your original equation was

\( f(x) = -4(\sin(2x + \pi)) - 5\)

We factored out the 2 so we have

\( f(x) = -4(\sin(2(x + \dfrac{\pi}{2})) - 5\)

So now it's in the same form as this

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
y = A sin(B(x + C)) + D

A is our amplitude
\(\text{period} = \dfrac{2\pi}{B}\)
phase shift is C. If it's +C then it's going to the left. If it's -C then it's going to the right
D is our vertical shift
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 20

What is the phase shift of \( f(x) = -4(\sin(2(x + \dfrac{\pi}{2})) - 5\)

Answer 21

thank you xiogonz
and i guess it would be x/2, AZ

Answer 22

Np

Answer 23

It's \(\Large\pi\) not x haha

Answer 24

wait i got it wrong

Answer 25

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
What is the phase shift of \( f(x) = -4(\sin(2(x + \dfrac{\pi}{2})) - 5\)
\(\color{#0cbb34}{\text{End of Quote}}\)
when you do something like
sin(x+1)
that ^^^ actually shifts 1 to the left

Answer 26

in that context, if you shift +pi/2 it wouldnt shift to the right, so that is not the phase shift

Answer 27

The font size, even in your question, is pretty small so the period looks like it's listed as x but it's \(\pi\)

Answer 28

ye lol

Answer 29

looks like an n* but it's actually \(\pi\)

Answer 30

oh breh, amplitude always positive, also \(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
What is the phase shift of \( f(x) = -4(\sin(2(x + \dfrac{\pi}{2})) - 5\)
\(\color{#0cbb34}{\text{End of Quote}}\)
when you do something like
sin(x+1)
that ^^^ actually shifts 1 to the left
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
in that context, if you shift +pi/2 it wouldnt shift to the right, so that is not the phase shift
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 31

---welp

Answer 32

Yes, since it's shifting to the left it's going to be negative

Answer 33

and amplitude is always positive

Answer 34

@snowflake0531

Answer 35

i think i forgot how to do these things again o-O

Answer 36

at least i still have my notes 😔