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Over which one of the following intervals is the function y=x^(2)-1 increasing?

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User Nilo
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1 Answer

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Firstly, let's analyze the function y = x^2 - 1. This is a quadratic function which draws a parabolic graph.

The degree of the x in this function is an even number (2) which means that the parabola would open upwards, resembling a "U" shape.

A parabolic function increases or decreases based on the direction of the opening. If it opens upwards (which is in our case), it initially decreases until its minimum point (vertex) and after that point, it starts increasing.

For our function y = x^2 - 1, the vertex will be at x = 0, because it is the root or zero for the function. Therefore, the function decreases for any x < 0 and starts increasing for x > 0.

Hence, for the function y = x^2 - 1, it increases over the interval (0, infinity). The interval of x where the function increases is from 0 till infinity.

Side note: (0, infinity) means not including 0, and continuing until infinity.

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User Solimanware
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