Final answer:
The domain of the relation r is {-2, -1, 0, 1, 3, 5}, and after calculating y = 2 - x for each x value, the range is {4, 3, 2, 1, -1, -3}. None of the provided options matches these sets exactly, possibly indicating an error in the options.
Step-by-step explanation:
To find the domain and range of the relation r, we can list out the values given for x and calculate the corresponding values for y using the equation y = 2 - x. Let's calculate the values one by one:
- For x = -2, y = 2 - (-2) = 4
- For x = -1, y = 2 - (-1) = 3
- For x = 0, y = 2 - 0 = 2
- For x = 1, y = 2 - 1 = 1
- For x = 3, y = 2 - 3 = -1
- For x = 5, y = 2 - 5 = -3
The domain of r is the set of all possible values of x, which in this case is given as {-2, -1, 0, 1, 3, 5}. The range of r is the set of all possible values of y that we have calculated, which is {4, 3, 2, 1, -1, -3}. To match the sets with the given options, we must order the range from greatest to smallest (or smallest to greatest), which gives us {4, 3, 2, 1, -1, -3}. However, this ordered set is not provided in the lettered options, which may indicate a typo in the provided options. The most correct answer based on our calculations would be:
Domain: {-2, -1, 0, 1, 3, 5}, Range: {4, 3, 2, 1, -1, -3}