Question

Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.

Answer 1

Answer:

First, we need to know when the function is increasing, and when is decreasing.

When a function is increasing, it's because to higher x-values belong higher y-values. On the other hand, a function is decreasing when to higher x-values belong lower y-values. The effect in the graph will be a upwards direction of the function when is increasing, and a downwards direction when is decreasing.

So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.

All these interpretations we can expressed using math language, specifically inequalities:

• 0 < x < 4: increasing.
• 4 < x < 6: decreasing.
• 6 < x < 8: increasing.
• 8 < x < 10: decreasing.
• 10 < x < 14: neither increasing or decreasing.