What is the range of the following function? {(4, 8), (9, 2), (-3, -4)}

Concept: For a relation given as a set of ordered pairs (x, y), the domain is the set of all first coordinates (the inputs), and the range is the set of all second coordinates (the outputs) that actually occur. Repeated values are listed only once, and the domain and range need not have the same number of elements.

Application: The given relation is {(4, 8), (9, 2), (-3, -4)}. Reading off the second coordinate of each pair gives the outputs 8, 2, and -4, so the range is {8, 2, -4}.

Contrast: Comparing the four sets offered:

• {4, 9, -3} collects the first coordinate of each pair - that is the domain, not the range.

• {8} keeps only one of the three outputs and drops the other two.

• {(4, 8), (9, 2), (-3, -4)} is the relation itself (the full set of ordered pairs), not the set of output values alone.

• {8, 2, -4} collects exactly the second coordinate of every pair - this matches the definition of range.

Result: The range of the function is {8, 2, -4}.