16
QuizMultiple Choice

Modeling Functions Using Finite Differences — Quiz

Question 16 • Algebraic Reasoning

Choose the function that represents the data in the table. x 0 1 2 3 4 5 f of x negative 7 193 393 593 793 993

Answer
A
f of x is equal to x to the 200th power minus 7
B
f of x is equal to 200 x squared minus 7
C
f of x is equal to 200 x minus 7
D
f of x is equal to 200 to the x th power minus 7

Explanation

Each time x increases by 1, f(x) increases by 200: −7, 193, 393, 593, 793, 993. This constant difference shows the data are linear, with slope 200. Since f(0) = −7, the function is f(x) = 200x − 7, choice C.

AI-written and checked against the verified answer.

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