Math Problem Statement

Analyze the graph of a function and identify its maximum, minimum, intervals of increase/decrease, domain, and range.

Solution

From the images you uploaded, here's what I can interpret:

First Image: Graph of the Function

  • The graph represents a smooth curve with two critical points marked:
    1. A maximum near x=1x = -1 where the function reaches its highest point on this segment.
    2. A minimum near x=3x = 3 where the function reaches its lowest point.

Second Image: Questions and Answers Based on the Graph

From the questions presented on the screen, it appears to be analyzing properties like:

  1. Maximum: The function reaches a maximum at x=1x = -1 with a value of 9.
  2. Minimum: The function reaches a minimum at x=3x = 3 with a value of -6.
  3. Intervals of increasing: From the graph, the function increases on the interval (,1)(-\infty, -1) and (3,)(3, \infty).
  4. Intervals of decreasing: The function decreases on the interval (1,3)(-1, 3).
  5. Domain: Since the graph extends infinitely in both directions, the domain appears to be (,)(-\infty, \infty).

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Math Problem Analysis

Mathematical Concepts

Calculus
Functions
Graph Analysis

Formulas

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Theorems

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Suitable Grade Level

High School (Grades 10-12)