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 all possible output values (i.e., the yy-values) that the function takes on.

By observing the graph:

  • The graph reaches a maximum yy-value of approximately 99.
  • The lowest point (minimum yy-value) appears to be around 9-9.
  • The graph covers all values in between these points without any gaps.

Thus, the range of the function can be written as: [9,9]\boxed{[-9, 9]}

Would you like further details or clarification on this? Here are some additional questions to deepen understanding:

  1. What is the definition of the domain of a function, and how would you find it for this graph?
  2. Can the range of a function ever be larger than its domain?
  3. How would you express the range if the graph extended indefinitely in either direction?
  4. How can you determine the range of a graph with vertical asymptotes?
  5. How would the range change if the function were shifted up by 5 units?

Tip: Always inspect the highest and lowest points of a graph when determining the range!

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Math Problem Analysis

Mathematical Concepts

Range of a function
Graph interpretation

Formulas

Range: The set of all possible output values (y-values)

Theorems

None explicitly required

Suitable Grade Level

Grades 9-12