Let f be a linear function with the properties that f(1)≤ f(2), f(3)≥ f(4), and f(5)=5. Which of the following statements is true?

1995 AMC 12 Problem 12

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12.

Let

f

be a linear function with the properties that

f(1)\le f(2),

f(3)\ge f(4),

and

f(5)=5.

Which of the following statements is true?

f(0)\lt0

f(0)=0

f(1)\lt f(0)\lt f(-1)

f(0)=5

f(0)\gt5

Translate each inequality into a condition on the slope

The two slope conditions together determine the entire linear function

From

f(1)\le f(2),

the slope is nonnegative. From

f(3)\ge f(4),

it is nonpositive. Thus the slope is

0,

f

is constant. Since

f(5)=5,

we have

f(0)=5.

Thus the correct answer is D.