Math Problem Statement

What are the domain and the range of the linear function shown in the graph?

Solution

The graph you've provided is a linear function, which is a straight line extending in both directions. To determine the domain and range, let's analyze the behavior of the line:

  1. Domain: The domain of a linear function is the set of all possible x-values the function can take. Since the line extends infinitely in both directions along the x-axis, the domain is all real numbers. This is expressed as: Domain:(,)\text{Domain}: (-\infty, \infty)

  2. Range: The range is the set of all possible y-values the function can take. Similarly, because the line continues infinitely in both the positive and negative directions along the y-axis, the range is also all real numbers: Range:(,)\text{Range}: (-\infty, \infty)

Would you like a detailed explanation of how the slope or specific points on the line relate to the equation of this linear function?


Here are some related questions you might explore:

  1. What is the equation of this linear function?
  2. How do you calculate the slope of the line?
  3. Can you determine the x- and y-intercepts from the graph?
  4. How does the slope affect the direction of the line?
  5. What are some real-life examples of linear functions?

Tip: When finding the domain and range of a linear function, remember that unless the function has restrictions (like vertical or horizontal lines), both the domain and range will be all real numbers!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Domain and Range

Formulas

General form of a linear equation: y = mx + b

Theorems

Properties of linear functions
Domain and range definitions

Suitable Grade Level

Grades 8-10