Math Problem Statement
The domain is the set of all real numbers. The range is y less than or equal to 5.
Solution
To determine the range of this function based on the graph:
- The line begins at when , and this point is marked with an open circle, meaning does not equal 6 at .
- The line decreases and ends at a point on the y-axis with when , marked with an arrow, which indicates that continues to decrease as moves right.
Therefore, the range of values is from upward to just below . Thus:
- Range: .
Would you like more details or have any questions?
Here are some follow-up questions to deepen understanding:
- How can we determine the slope of the line from the graph?
- What would the range be if the line extended infinitely in both directions?
- How would an open versus closed endpoint affect the range?
- How would the range change if the line had a positive slope?
- What is the range if we consider the line extending only to certain x-values?
Tip: When determining the range, always check both the highest and lowest points the graph reaches.
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Math Problem Analysis
Mathematical Concepts
Graphing
Linear Functions
Domain and Range
Formulas
y = mx + b
Theorems
Concept of domain and range
Suitable Grade Level
Grades 7-9