Oklahoma State Standards Practice Test

Given f defined by f(1)=4, f(2)=5, f(3)=6, which statements are true about this mapping?

It is a function and linear with f(x) = x + 3 for x in {1,2,3} It is a function but not linear It is not a function It is neither a function nor linear

Correct Answer:

It is a function and linear with f(x) = x + 3 for x in {1,2,3}

Explanation:

The mapping assigns exactly one output to each input, so it is a function. The outputs follow a simple pattern: each time the input increases by 1, the output increases by 1 as well, and the difference between output and input is constant at 3. That means the rule f(x) = x + 3 fits all the given pairs (1→4, 2→5, 3→6). On this domain {1, 2, 3}, that makes the mapping linear. Therefore, it is both a function and linear with f(x) = x + 3 for these inputs.

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