Math Problem Statement

How would you describe the behavior of this function on the domain interval (-1, 1)?

Solution

The graph in the image shows a piecewise function, and you are asked to describe its behavior on the domain interval (1,1)(-1, 1).

From the graph:

  • The function is constant between x=1x = -1 and x=1x = 1, as the line is flat at y=1y = 1 for that portion of the domain. This suggests that the function does not increase or decrease; instead, it stays at a fixed value.

Thus, the correct answer is "constant" for the behavior on the interval (1,1)(-1, 1).

Would you like further details on this or have any questions?

Here are five related questions to explore:

  1. How would the function behave outside the interval (1,1)(-1, 1)?
  2. What is the definition of a constant function?
  3. How can you determine if a function is increasing or decreasing from a graph?
  4. How does the slope of a line relate to whether a function is increasing, decreasing, or constant?
  5. Can a function be both increasing and decreasing in different intervals?

Tip: A constant function means that for any change in xx, the value of yy remains the same.