Question

f(x)=-3/2cos(3x+4pi)+5

Find The Period, Range, Phase Shify, and Vertical Shift.

Answer 1

@roadjester

Answer 2

\(\Large f(x) = -\dfrac {3} 2 cos(3x+4\pi)\)+5 correct?

Answer 3

Yes sir

Answer 4

ok so standard form is a*cos(bx+c)+d

Answer 5

Isn't already in that form?..

Answer 6

exactly

Answer 7

now, once it's in that form, you're given all the information you were asked to look for

Answer 8

let's start with the easiest two, amplitude and vertical shift

Answer 9

amplitude of a sin/cos function is simply "a"
and the vertical shift is simply "d"

Answer 10

Amplitude is -3/2

Answer 11

make sense

Answer 12

Si senor

Answer 13

whoops, ok my mistake

Answer 14

Go Get Your Dinner

Answer 15

amplitude is |a|

Answer 16

so in this case, the graph will go up 1.5 units and down 1.5 units

Answer 17

the negative sign means it's been flipped upside -down

Answer 18

OOOhhh, Got You

Answer 19

The vertical shift is 5?

Answer 20

ok the vertical shift itself depends only on the |d|, but the direction it is shifted vertically depends on the sign

Answer 21

Ummm...

Answer 22

think of it this way, when you have y=mx+b

Answer 23

the b is your y intercept and it is also your vertical shift; make sense?

Answer 24

only if i could understand

Answer 25

umm ok have you ever seen a sine or cosine wave before?

Answer 26

so is it 4

Answer 27

That's the shape of your standard cosine wave