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.

Next Contents: Quadratic Function