To identify the domain and range of a mathematical function, let's break it down:

1. Domain: This refers to all the possible input values (x-values) for which the function is defined.
2. Range: This refers to all the possible output values (y-values) that the function can take.

If you provide the function or context (e.g., a graph, equation, or real-world scenario), I can determine the domain and range explicitly.

For now, here are general principles for common functions:

• Polynomials:
  Domain: All real numbers
  Range: Depends on the degree and coefficients.

• Rational functions (fractions):
  Domain: All real numbers except where the denominator is 0.
  Range: Depends on the behavior of the function and any vertical or horizontal asymptotes.

• Square root functions:
  Domain: Values where the radicand (expression under the square root) is non-negative.
  Range: Non-negative real numbers if no shifts occur.

• Trigonometric functions:
  Domain and range vary (e.g., $\sin(x)$: Domain = all real numbers; Range = $[-1, 1]$).

Please provide the function or graph for precise analysis!

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Would you like help with a specific function?

Here are 5 follow-up questions you might consider:

1. What is the domain and range of the function $f(x) = \frac{1}{x+2}$?
2. Can you explain how vertical asymptotes affect the domain?
3. How do transformations like shifting or stretching impact the range of a function?
4. What is the difference in domain for even vs. odd root functions?
5. How do we determine the domain of a composite function?

Tip: When finding the domain of a function, always look for points where the function could be undefined, such as division by zero or negative square roots.