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].
- For x = 1, y = 2(1) - 5 = 2 - 5 = -3.
- For x = 2, y = 2(2) - 5 = 4 - 5 = -1.
- 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.