A function is a relation in which every input has exactly one output.
Which choice represents a function?
(−4, 3), (7, 2), (−5, 4), (9, 5), (−4, 2), (0, 1)
y = 2^x
x ± √x − 2 → k(x)
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A function is a relation in which every input has exactly one output.
Which choice represents a function?
(−4, 3), (7, 2), (−5, 4), (9, 5), (−4, 2), (0, 1)
y = 2^x
x ± √x − 2 → k(x)
To determine which choice represents a function, we need to check if every input (first element of each pair or the variable in the equation) has exactly one output (second element of each pair or the output of the function).
1. For the pair representation:
The pairs are (−4, 3), (7, 2), (−5, 4), (9, 5), (−4, 2), (0, 1).
Here, the input −4 is repeated with two different outputs (3 and 2). This means it does not represent a function.
2. For the equation (y = 2^x):
This is a function because for each input x, there is exactly one output y.
3. For (k(x) = x ± √(x − 2)):
This expression can yield two outputs for the same input (for example, if you input a value where the square root is defined, you’ll get one output for plus and one for minus). This does not represent a function.
Thus, the only choice that represents a function is (y = 2^x).
Answer: y = 2^x; it represents a function since for each input x, there is exactly one output y.