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Find the range for y = 2x - 5, if the domain is 1, 2, 6.

a) [-3, 7, 17]
b) [-3, 9, 17]
c) [-5, 3, 7]
d) [-5, 7, 17]

1 Answer

4 votes

Final answer:

The range for the function y = 2x - 5 with the domain of 1, 2, 6 is calculated by substituting each x into the function, resulting in the range {-3, -1, 7}. None of the given options match this correct range. Therefore, none of the given options a) [-3, 7, 17], b) [-3, 9, 17], c) [-5, 3, 7], or d) [-5, 7, 17] are correct because none of them contain all three correct values of the range we found.

Step-by-step explanation:

To find the range for the function y = 2x - 5 with the domain of 1, 2, 6, we calculate the value of y for each x in the domain.

The range of a function represents the set of all possible output values. To find the range of the function y = 2x - 5, we need to determine the range of the given domain values. Let's substitute each domain value into the function and see what output values we get:

Therefore, the range of the function is [-3, -1, 7].

  1. For x = 1, y = 2(1) - 5 = 2 - 5 = -3.
  2. For x = 2, y = 2(2) - 5 = 4 - 5 = -1.
  3. For x = 6, y = 2(6) - 5 = 12 - 5 = 7.

The range is the set of all y values we just calculated, so the range is {-3, -1, 7}. Therefore, none of the given options a) [-3, 7, 17], b) [-3, 9, 17], c) [-5, 3, 7], or d) [-5, 7, 17] are correct because none of them contain all three correct values of the range we found.

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