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

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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 x
_{1}<x_{2}then ax_{1}<ax_{2}. Hence, ax_{1}+ b <ax_{2}+ b, where does f come from (x_{1}) <f (x_{2}). - for a <0: if x
_{1}<x_{2}then ax_{1}> ax_{2}. Hence, ax_{1}+ b> ax_{2}+ b, where does f come from (x_{1})> f (x_{2}).