Math Problem Statement

Determine the range of the following graph.

Solution

To determine the range of the given graph, we need to observe the values of yy that the graph takes.

  • The graph has an upper point at y=11y = 11 (where the curve starts) and it decreases from there.
  • The lowest point occurs near y=10y = -10, and the graph seems to level out just above y=9y = -9.
  • Hence, the range of the graph consists of all values between 10-10 and 1111.

Thus, the range of the graph is: y[10,11]y \in [-10, 11]

Would you like more details or have any questions?

Here are 5 questions to expand on the topic:

  1. How do you determine the range of a function algebraically?
  2. What is the difference between domain and range in a function?
  3. How can graph transformations affect the range?
  4. What are some examples of functions with restricted ranges?
  5. How do asymptotes affect the range of a function?

Tip: Always check both the highest and lowest points of the graph to find the range effectively.

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Range of Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12