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Increasing or decreasing function


Consider the function of the 1st degree y = 3x-1. Let's assign increasing values ​​to x and observe what happens to y:

x-3-2-10123
y-10-7-4-1258

Note that when we increase the value of x, the corresponding values ​​of y also increase. We then say that the function y = 3x - 1 is increasing. Look at your chart:

General rule:

- the function of the 1st degree f (x) = ax + b is growing when the coefficient of x is positive (a> 0);
- the function of the 1st degree f (x) = ax + b is descending when the coefficient of x is negative (a <0);

Justification:

  • for a> 0: if x1 <x2then ax1 <ax2. Hence, ax1 + b <ax2 + b, where does f come from (x1) <f (x2).
  • for a <0: if x1 <x2then ax1 > ax2. Hence, ax1 + b> ax2 + b, where does f come from (x1)> f (x2).
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