Math Problem Statement

Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?

Solution

To determine which table shows a function that is increasing only over the interval (-2, 1) and nowhere else, let’s break this down:

  1. A function is increasing on an interval if the values of f(x)f(x) increase as xx moves from left to right in that interval.
  2. Outside the interval (2,1)(-2, 1), the function should not be increasing. It may be constant or decreasing.

Characteristics of the correct table:

  • f(x)f(x) increases only for xx values between 2-2 and 11.
  • f(x)f(x) does not increase for x<2x < -2 or x>1x > 1.
  • For points outside the interval (2,1)(-2, 1), f(x)f(x) values must either stay the same or decrease.

Do you have a specific set of tables or values? If not, I can help generate a table for this situation. Let me know!


If you’d like, I can explain more about functions and intervals. Here are 5 related questions:

  1. How do you test if a function is increasing or decreasing from a graph?
  2. What is the difference between increasing and strictly increasing?
  3. Can a function be increasing at a single point, like x=2x = -2?
  4. How would a derivative help verify whether a function increases on a specific interval?
  5. What happens if a function is constant outside (2,1)(-2, 1)?

Tip: When checking for increasing intervals, focus on the pattern of the outputs (f(x)f(x)) and how they change as the inputs (xx) progress.

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Math Problem Analysis

Mathematical Concepts

Functions
Intervals
Increasing and Decreasing Behavior of Functions

Formulas

None (Focus is on identifying increasing behavior from tabulated values)

Theorems

None (Basic principles of increasing functions are applied)

Suitable Grade Level

Grades 9-11