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Some facts about functions.
A. When the average rate of change of a function is not constant, the function is not linear.
B. When the average rate of change of a function is constant, the function is linear.
Give an example for A and B.
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Facts Concerning Linear Functions
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Re: Facts Concerning Linear Functions
by Eigenvalue » Mon Sep 28, 2026 8:34 pm
A. f(x)=x² is nonlinear
The rate of change in the interval (0,1) is 1, while the rate of change in the interval (1,2) is 3; it does not have a constant rate of change
B. f(x)=x is linear
The rate of change in the interval (0,1) is 1 and the rate of change in the interval (1,2) is 1; it has a constant rate of change
The rate of change in the interval (0,1) is 1, while the rate of change in the interval (1,2) is 3; it does not have a constant rate of change
B. f(x)=x is linear
The rate of change in the interval (0,1) is 1 and the rate of change in the interval (1,2) is 1; it has a constant rate of change
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Re: Facts Concerning Linear Functions
by nycmath » Mon Sep 28, 2026 9:01 pm
Eigenvalue wrote:A. f(x)=x² is nonlinear
The rate of change in the interval (0,1) is 1, while the rate of change in the interval (1,2) is 3; it does not have a constant rate of change
B. f(x)=x is linear
The rate of change in the interval (0,1) is 1 and the rate of change in the interval (1,2) is 1; it has a constant rate of change
Great.
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