Question

Consider the function y = f(x) shown at right, trace each interval where the function behavior is A. Increasing, using a GREEN pencil Identify the interval(s) ___B. Decreasing, using a RED pencil Identify the interval(s) ___ C. Constant, using a YELLOW pencil Identify the interval(s) ___ D. State the Domain of the function ___ E. State the Range of the function ___ F. What thoughts do you have about the intervals stated above? Did you use brackets (closed/included points) or parentheses (open/non-included points)? Why or why not?

Answer 1

You have a function f(x). To identify the increasing interval and decreasing interval of f(x), you consider that an increasing interval is determined by the values of x in which the value of f(x) increases. For the decreasing interval you focus on the values of x in which the values of f(x) decreases.

You can notice in the given graph:

The increasing interval is (-8 , -4) U (3 , 6)

The decreasing interval is (-4 , -2)

The constant interval is (-2 , 3)

The domain of the function is (-8 , 6)

The previous interval is given by the available values of x

The range of the function is (-4 , 8)

The previos interval is given by the values of f(x) for the values of x in the domain.

The following image is a sketch of the graph with the respective intervals.