Question

MAX POINTS PLEASE HELP Will make Brainliest

Answer 1

Answer:

Period: 6, Frequency: 1/6, Equation: -4cos($\frac{\pi }{3}x$)-2

Step-by-step explanation:

Because the graph starts at x = 0 at a minimum/maximum, it's easiest to use cosine, so we don't have to shift the graph horizontally. cos(x)

If you take the max/min points and average them, you can use the distance between the average value and the max/min to get the total amplitude, A, which is 4.

Because this function starts at a minimum, but cosine starts at a maximum, we will flip it vertically by adding a negative coefficient to whatever the amplitude is.

We see that the same part of the graph recurres every 6 x-units, so the period is 6. The frequency of this is 1/(period), 1/6.

The coefficient of x in a sin/cos function is $2\pi /Period$, = $\pi$/3.

The vertical shift (how much the average value of the function moved from 0 to its current position) is -2.

Put all that together, you get y = -4cos($\frac{\pi }{3}x$)-2

Answer 2

$\qquad\qquad\huge\underline{{\sf Answer}}♨$

let's solve ~

Period :

Difference between two successive crest or trough is known as period, so here :

period = 9 - 3 = 6

Frequency

Now, we know that frequency = 1/period

So, frequency for given function is 1/6 hertz , or approximately 0.167 hertz

• Amplitude (A) = 4 (flipped)

• b = 2π ÷ Period = 2π /6 = π/3

• k = -2

The required equation is ~

$\qquad \sf \dashrightarrow \:y = a \cos(bx) + k$

$\qquad \sf \dashrightarrow \:y = - 4 \cos( \frac{ \pi}{3} x) - 2$