Math Problem Statement

Find the domain and range of the function shown in the graph. Remember, if the curve touches the edge of the graph, assume it continues in that direction forever.

Solution

The graph provided shows a straight line, which appears to be a linear function with a negative slope, and it extends indefinitely in both directions, touching the edges of the graph.

Domain and Range:

  1. Domain: The domain refers to all the possible input values (x-values) of the function. Since the line extends infinitely in both directions horizontally (and is not restricted by any breaks or asymptotes), the domain is all real numbers.

    • Domain: (,)(-\infty, \infty)
  2. Range: The range refers to all the possible output values (y-values) of the function. Similar to the domain, the line extends infinitely in both directions vertically, covering all y-values.

    • Range: (,)(-\infty, \infty)

Conclusion:

  • Domain: (,)(-\infty, \infty)
  • Range: (,)(-\infty, \infty)

Would you like more details on how to interpret domains and ranges for different types of functions?

Here are 5 related questions:

  1. How do you find the slope of a linear function from a graph?
  2. What is the difference between the domain and range in a function?
  3. How do the domain and range change if the function is a parabola instead of a line?
  4. How would the domain and range be affected if the function had an asymptote?
  5. Can a function have a restricted domain and range even if it looks like a straight line?

Tip: For linear functions, always check for breaks in the graph or any restrictions that may limit the domain or range.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10