Math Problem Statement

Determine the range of the following graph:

Solution

To determine the range of the given graph, we need to identify the set of possible output values (i.e., the yy-values) that the function takes.

Analyzing the Graph:

  1. Maximum yy-value: The graph appears to reach a maximum point at around y=7y = 7.
  2. Minimum yy-value: The graph appears to reach a minimum point at around y=10y = -10.
  3. The graph spans vertically from y=10y = -10 to y=7y = 7, and it seems that all yy-values between these two extremes are included.

Conclusion:

The range of the graph is from 10-10 to 77, inclusive. Therefore, the range can be written as: [10,7][-10, 7]

Would you like more details, or do you have any other questions about this?

Here are 5 related questions to expand on this concept:

  1. What is the domain of the graph?
  2. How can you determine if a function is continuous from its graph?
  3. What is the significance of the maximum and minimum points on a graph?
  4. How would the range change if the graph was shifted up or down?
  5. What is the difference between the range and the codomain of a function?

Tip: When determining the range of a graph, always check the highest and lowest points of the graph to ensure you capture all possible output values.

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Math Problem Analysis

Mathematical Concepts

Range of a Function
Graph Analysis

Formulas

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Theorems

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Suitable Grade Level

Grades 9-11