For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response.

Question

Use the sequence a_n=7n-5 for Part A, Part B, and Part C. 

Part A: If the range value is 16, what is the domain value? Show your work. 

Part B: If the range value is 58, what is the domain value? Show your work. 

Part C: Hunter says that the domain value is 6 when the range value is  37. Is Hunter correct? Explain why or why not, and show your work to support your answer. 

Answer 1

Part A: If the range value is 16, what is the domain value? Show your work.

To find the corresponding domain value when the range is 16, we can use the sequence formula a_n = 7n - 5.

16 = 7n - 5

Adding 5 to both sides:

21 = 7n

Dividing both sides by 7:

n = 3

Therefore, when the range value is 16, the domain value (n) is 3.

Part B: If the range value is 58, what is the domain value? Show your work.

Using the same sequence formula a_n = 7n - 5, we can find the domain value for a given range of 58.

58 = 7n - 5

Adding 5 to both sides:

63 = 7n

Dividing both sides by 7:

n = 9

So, when the range value is 58, the corresponding domain value (n) is 9.

Part C: Hunter says that the domain value is 6 when the range value is 37. Is Hunter correct? Explain why or why not, and show your work to support your answer.

To verify if Hunter is correct, we need to substitute the given range value (37) into the sequence formula and check if it corresponds to the domain value of 6.

37 = 7n - 5

Adding 5 to both sides:

42 = 7n

Dividing both sides by 7:

n = 6

Since n = 6 matches the given domain value of 6, Hunter is indeed correct. When the range value is 37, the corresponding domain value is 6.

Answer 2

The sequence a_n = 7n - 5 is really a function. When the input is a number n, the output is 7n - 5. For example, a_3 = 7*3 - 5 = 21 - 5 = 16. By "range value" they mean "output" and by "domain value" they mean "input".

For part A, the question is: "What is the input when the output is 16?" In other words, if 7n - 5 = 16, then what must n be? We can solve this equation.

7n - 5 = 16

7n = 21

n = 3

For part B, similarly we have to solve 7n - 5 = 58. Again we can write:

7n - 5 = 58

7n = 63

n = 9

For part B we need to check if Hunter is right that a_6 = 37, or in other words if 7*6 - 5 = 37. We can check that this is true: 7*6 = 42 and 42 - 5 = 37.