write the equation of the function represented by the following graph medal

- anonymous

write the equation of the function represented by the following graph medal

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- anonymous

##### 1 Attachment

- jim_thompson5910

See if you can determine
* The amplitude
* The period

- anonymous

3 and pi/4

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## More answers

- jim_thompson5910

The period is actually pi/2

- jim_thompson5910

But you have the right amplitude

- anonymous

got it then what next

- jim_thompson5910

The y-intercept is not 0, and the relative extrema is at the y-intercept, so we have a cosine function here
Since the y-intercept is negative, this means that the cosine function has a negative coefficient

- jim_thompson5910

General form
y = A*cos(Bx-C)+D
C = 0 and D = 0, so don't worry about those
|A| = amplitude
T = 2pi/B is the period

- jim_thompson5910

with T = 2pi/B you can solve for B to get
B = 2pi/T
plug in the period T=pi/2 and simplify

- anonymous

b=0 and t=0? @jim_thompson5910

- jim_thompson5910

T = pi/2 is the period
its not t = 0

- jim_thompson5910

\[\Large B = \frac{2\pi}{T}\]
\[\Large B = \frac{2\pi}{\pi/2}\]
\[\Large B = ??\]

- anonymous

b= 90 degrees

- jim_thompson5910

idk how you're getting that

- anonymous

http://www.wolframalpha.com/input/?i=+pi%2F2

- anonymous

0

- jim_thompson5910

can you simplify this expression?
\[\Large \frac{2\pi}{\pi/2}\]

- anonymous

1

- jim_thompson5910

not quite

- jim_thompson5910

\[\Large \frac{2\pi}{\pi/2} = \frac{2\pi}{1} \times \frac{2}{\pi} = ???\]

- anonymous

0

- anonymous

@jim_thompson5910

- jim_thompson5910

no, forget about the pi
think of the pi as x if you have to

- jim_thompson5910

2x/1 times 2/x simplifies to what?

- anonymous

4

- jim_thompson5910

so B = 4

- jim_thompson5910

what is A?

- anonymous

1

- jim_thompson5910

no, remember that above I said that |A| = amplitude
and you said earlier that the amplitude was 3

- anonymous

sorry it 3

- jim_thompson5910

it's actually -3 to make sure that the y-intercept is -3

- jim_thompson5910

so
A = -3
B = 4

- jim_thompson5910

y = A*cos(Bx-C)+D
A = -3
B = 4
C = 0
D = 0

- anonymous

so its y=-3cos(4x):)

- anonymous

y=-3cos(4x) is the answer

- jim_thompson5910

yes correct

- anonymous

thanks so much !!!

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