Math Problem Statement

List the interval(s) on which f is increasing.

Solution

To determine the intervals on which the function is increasing from the graph you provided, I'll analyze the sections of the graph where the function values rise as the xx-values increase from left to right.

From the graph, the function is increasing in these intervals:

  • From approximately x=10x = -10 to x=8x = -8
  • From approximately x=3x = -3 to x=1x = -1
  • From approximately x=2x = 2 to x=4x = 4
  • From approximately x=7x = 7 to x=10x = 10

Using interval notation:

  • (10,8)(-10, -8)
  • (3,1)(-3, -1)
  • (2,4)(2, 4)
  • (7,10)(7, 10)

Would you like any additional details on how these intervals were determined or help with another part of the graph? Here are some additional topics we could explore:

  1. How to determine when a function is decreasing.
  2. How to identify local maxima and minima from a graph.
  3. The concept of concavity and points of inflection.
  4. How to sketch a derivative based on the graph of a function.
  5. The importance of scale and accuracy in reading graphs.

Tip: When identifying intervals of increase or decrease from a graph, look for the direction of the y-values as x increases; an upward trend indicates increasing intervals.

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Math Problem Analysis

Mathematical Concepts

Calculus
Graph Analysis
Increasing/Decreasing Functions

Formulas

-

Theorems

Intermediate Value Theorem

Suitable Grade Level

Grades 9-12