Math Problem Statement

What are the domain and range of the line shown in the graph?

Solution

The graph you uploaded shows a straight line on a coordinate plane. To determine the domain and range of this linear function, we analyze the characteristics of the line:

  1. Domain: The domain refers to all possible values of xx. Since the line extends infinitely in both horizontal directions (left and right), the domain includes all real numbers.

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

  2. Range: The range refers to all possible values of yy. Similarly, because the line extends infinitely in both vertical directions (up and down), the range also includes all real numbers.

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

Would you like further details on the graph's equation or any other aspect?

Here are 5 related questions to expand this topic:

  1. How do you find the equation of a line given its graph?
  2. How can you determine the slope of a line by looking at its graph?
  3. What is the relationship between the slope of a line and its steepness?
  4. How does changing the slope or intercept affect the appearance of a line on a graph?
  5. How do domain and range differ for non-linear functions?

Tip: When analyzing straight lines, always check if they extend infinitely in both directions to determine their domain and range, as most lines will have a domain and range of all real numbers unless restricted.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

None needed for domain and range determination of linear functions

Theorems

None needed for domain and range determination of linear functions

Suitable Grade Level

Grades 8-10