AMC12 2003 B

AMC12 2003 B · Q9

AMC12 2003 B · Q9. It mainly tests Linear equations, Functions basics.

Let $f$ be a linear function for which $f(6) - f(2) = 12.$ What is $f(12) - f(2)?$

设 $f$ 是一个一次函数，且 $f(6) - f(2) = 12.$ 求 $f(12) - f(2)$。

(A) 12 12

(B) 18 18

(D) 30 30

(E) 36 36

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since $f$ is a linear function with slope $m$, \[m = \frac{f(6) - f(2)}{\Delta x} = \frac{12}{6 - 2} = 3\] \[f(12) - f(2) = m \Delta x = 3(12 - 2) = 30 \Rightarrow \text (D)\]

由于 $f$ 是一次函数，斜率为 $m$， \[m = \frac{f(6) - f(2)}{\Delta x} = \frac{12}{6 - 2} = 3\] \[f(12) - f(2) = m \Delta x = 3(12 - 2) = 30 \Rightarrow \text (D)\]

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