Math Problem Statement

Determine the range of the following graph:

Solution

The task is to determine the range of the given graph.

Step-by-step solution:

  1. Definition of Range: The range of a function is the set of all possible yy-values (outputs) that the function can take. To find the range, observe the vertical extent of the graph.

  2. Analyzing the Graph:

    • The graph has a minimum yy-value at approximately 10-10 (the lowest point of the curve).
    • The graph extends upwards to a maximum yy-value of 1010, as indicated by the open circle near y=10y = 10.
    • The open circle at y=10y = 10 shows that y=10y = 10 is not included in the range.
    • The graph continues smoothly between y=10y = -10 and y=10y = 10, so all yy-values in this interval are included except 1010.
  3. Conclusion: The range of the graph is: [10,10)[-10, 10) This means yy can take any value from 10-10 to 1010, including 10-10 but excluding 1010.


Do you have any questions or want further clarification?

Related Questions:

  1. What is the difference between the range and domain of a function?
  2. How would the range change if the open circle at y=10y = 10 were filled?
  3. Can the range of a graph include gaps or discontinuities? Explain with examples.
  4. How can you determine if a graph has an open or closed interval for its range?
  5. How does the behavior of the graph near the edges influence the range?

Tip:

When identifying the range of a function, always check for open or closed points and note whether the graph extends infinitely or is bounded within a specific interval.

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Math Problem Analysis

Mathematical Concepts

Range of a Function
Graphs of Functions

Formulas

-

Theorems

Range Definition

Suitable Grade Level

Grades 9-11