money2690
Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

MAX POINTS PLEASE HELP Will make Brainliest

What is the period and frequency of the function graphed and how would the equation be written??

MAX POINTS PLEASE HELP Will Make Brainliest What Is The Period And Frequency Of The Function Graphed And How Would The Equation Be Written class=

Sagot :

Answer:

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

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

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 ~

[tex]\qquad \sf  \dashrightarrow \:y = a \cos(bx) + k[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = - 4 \cos( \frac{ \pi}{3} x) - 2[/tex]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.