If f is a linear function and f(2) > f(3), which of the follwoing must be true ?A.f(-2) > f(-3)B.f(-1) > f(1)C.f(0) > f(-1)D.f(3) > f(-2)
Question
If f is a linear function and f(2) > f(3), which of the follwoing must be true ?A.f(-2) > f(-3)B.f(-1) > f(1)C.f(0) > f(-1)D.f(3) > f(-2)
Solution
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
If f(2) > f(3), this means that as x increases, f(x) decreases. This implies that the slope m of the function is negative.
A. f(-2) > f(-3): This must be true. If the slope is negative, as x decreases (from -2 to -3), f(x) increases.
B. f(-1) > f(1): This must be true. If the slope is negative, as x increases (from -1 to 1), f(x) decreases.
C. f(0) > f(-1): This must be true. If the slope is negative, as x increases (from -1 to 0), f(x) decreases.
D. f(3) > f(-2): This must be false. If the slope is negative, as x increases (from -2 to 3), f(x) decreases.
So, the correct answer is A, B, and C.
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