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Sign of 1st degree function


Studying the sign of any function y = f (x) is to determine the values ​​of x for which y is positive, the values ​​of x for which y is zero, and the values ​​of x for which y is negative.

Considering an affine function y = f (x) = ax + b, let's study its signal. We already saw that this function cancels to the root . There are two possible cases:

1º) a> 0 (the function is increasing)

y> 0 ax + b> 0 x>

y <0 ax + b <0 x <

Conclusion: y is positive for x values ​​greater than the root; y is negative for x values ​​less than root

2º) a <0 (the function is decreasing)

y> 0 ax + b> 0 x <

y <0 ax + b <0 x>

Conclusion: y is positive for x values ​​less than the root; y is negative for x values ​​greater than the root.

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