T={(2,4),(−5,1),(2,0),(2,−2)}

Question

determine if the relation is a function. If it is not, identify two ordered pairs as proof.

Answer 1

These relations prove that f(x) is not a function of x:

x f(x)

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2 4

2 0

2 -2

These ordered pairs are not allowed because each valid input (that is, each x) must produce exactly one output (that is, an f(x)) in order for f(x) to be a function of x.

Answer 2

For a relation to be a function for every x input there can be ONE AND ONLY ONE y output

In this example for the x input there are 3 possible y outputs 4, 0 and -2.

The ordered pairs (2,4) and (2,0) would serve as proof