Question

Use the graph of f to find the largest open interval on which f is increasing, and the largest open interval on which f is decreasing. (Enter your answers using interval notation.)

Answer 1

a. The largest open intervals on which f is increasing are (0, 4), (6, 9).

b. The largest open interval on which f is decreasing are (4, 6), (9, 10).

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

Part a.

By critically observing the graph of this polynomial function above, we can reasonably and logically deduce that it is increasing over the following open intervals;

increasing = (0, 4), (6, 9).

Part b.

For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of this polynomial function above, we can reasonably and logically deduce that it is decreasing over the following open intervals;

decreasing = (4, 6), (9, 10).