Math Problem Statement

Determine the domain of the following graph:

Determine the domain of the following graph:

Solution

To determine the domain of the given graph, we need to identify the range of x-values for which the graph is defined.

Upon examining the graph:

  • The curve starts at x=11x = -11 (where the point is approximately at (11,2)(-11, -2)).
  • The curve ends at x=6x = 6 (where the point is approximately at (6,4)(6, -4)).

Thus, the domain is the set of x-values from -11 to 6, inclusive.

Therefore, the domain of the graph is: [11,6][-11, 6]

Would you like further details or clarifications on how this was determined?

Here are five related questions to expand on this:

  1. What is the range of the function represented by this graph?
  2. Can you determine the function type based on this graph's behavior?
  3. How would you find the x-intercepts and y-intercepts of the graph?
  4. Is this graph continuous, and why does that matter for domain and range?
  5. What transformations could you apply to this function, and how would it affect the graph?

Tip: The domain of a graph represents all possible x-values where the function is defined, while the range corresponds to all possible y-values. Always check both when analyzing graphs!

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Math Problem Analysis

Mathematical Concepts

Functions
Domain of a function
Graph analysis

Formulas

-

Theorems

Domain of a function

Suitable Grade Level

Grades 9-11