Question

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Answer 1

Answer: d) increasing from -2 to 0 and 3/2 to ∞

decreasing from -∞ to -2 and 0 to 3/2

Explanation:

Graph the equation. Then follow the path of the curve from left to right. If you are going down, then it is decreasing. If you are going up, then it is increasing.

See image below. Blue represents decreasing. Red is increasing.

Note: If you are unable to graph the equation, then find the zeros of the equation, choose test points between the zeros, and plug them into the equation. If the test point is negative, then it is decreasing. If the test point is positive, then it is increasing.

Answer 2

Last option: increasing: -2 < x < 0 and x> 3/2;

decreasing: x < -2 and 0 < x < 3/2

Explanation:

The function given is an absolute cubic function. (Pictured below).

We can determine from the graph that the equation increases over the interval:

increasing: -2 < x < 0 and x> 3/2;

decreasing: x < -2 and 0 < x < 3/2