The linear function f of x is defined on the interval left bracket 1 comma 3 right bracket such that f of 1 is equal to 3 and f of 3 is equal to 7 How much does f of x increase when x increases by 1 ?

For a linear function, the increase in f(x) for each 1-unit increase in x is its slope. Using the given points, the slope is (7 − 3) ÷ (3 − 1) = 4 ÷ 2 = 2. Therefore, f(x) increases by 2 when x increases by 1; the correct choice is 2.

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