Math Problem Statement

What is the range of the function shown in the graph below?

Solution

From the graph shown in your image, we can observe the following behavior of the function:

  • The graph reaches a maximum value slightly above y=10y = 10.
  • The graph reaches a minimum value slightly below y=10y = -10.
  • The graph extends infinitely upwards (as indicated by the arrow at the top) and downwards (as indicated by the arrow at the bottom).

Given these observations, the function seems to cover all real numbers vertically, meaning the range of the function is all real values of yy.

Thus, the range of the function is: (,)(-\infty, \infty)

Would you like more details or explanations on how ranges are determined?

Here are some additional questions for further exploration:

  1. How can you determine the domain of a function from its graph?
  2. What is the difference between the domain and range of a function?
  3. Can a function have a finite range but an infinite domain?
  4. How can horizontal and vertical asymptotes affect the range of a function?
  5. What role does the vertex play in determining the range of quadratic functions?

Tip: Always look for arrows in graphs to identify whether the function extends to infinity.

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Math Problem Analysis

Mathematical Concepts

Functions
Range of a Function
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10