What is the domain and range of the relation shown in the table?
1 answer:
Answer:
<u>domain: {10,15,19,32}</u>
<u>range:{5,9,-1}</u>
Step-by-step explanation:
- As we know domain is the values of input and range is the values of output.
- Here , x is the input and y is the output.
- Thus the input values according to the given problem is : 10 ,15 , 19, and thus ,
⇒<em>The domain would accordingly be these four numbers : 10 , 15 , 19 , 32.</em>
- <u>Note that we donot have any information regarding the other values of x.</u>
- The range is : { 5,9,-1 } only as the 5 is repeated in two cases .
- Range is unique and there must be not repetition. Thus the apt answer would be :
<em>domain: {10,15,19,32}</em>
<em>range:{5,9,-1}</em>
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Step-by-step explanation:
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A sine function is represented as:
![y =A \sin(Bx + C) + D](https://tex.z-dn.net/?f=y%20%3DA%20%5Csin%28Bx%20%2B%20C%29%20%2B%20D)
Where
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By comparing:
and ![y = -\frac{1}{3} * \sin(x - \frac{1}{3})](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Csin%28x%20-%20%5Cfrac%7B1%7D%7B3%7D%29)
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![B = 1](https://tex.z-dn.net/?f=B%20%3D%201)
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![Period = \frac{2\pi}{B}](https://tex.z-dn.net/?f=Period%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BB%7D)
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Hence, the period of the function is ![2\pi](https://tex.z-dn.net/?f=2%5Cpi)