Math Problem Statement
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:
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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:
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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:
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:
- What is the equation of this linear function?
- How do you calculate the slope of the line?
- Can you determine the x- and y-intercepts from the graph?
- How does the slope affect the direction of the line?
- 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