Math Problem Statement
This is the graph of a linear function. What is the range of the function? Write your answer as an equation like x=5, as an inequality like y>3, or as a compound inequality like 2≤x<4.
Solution
To determine the range of the given linear function, let's analyze the graph provided.
Observations:
- The line segment is located in the lower-right part of the graph.
- The segment begins at around and and ends near and .
- As increases from 5 to 9, decreases linearly.
Range of the Function:
The range of the function corresponds to the set of all possible -values the graph covers. From the graph:
- The lowest -value is -8 (at ).
- The highest -value is -6 (at ).
Thus, the range of the function is:
Final Answer:
The range is .
Do you need further clarification or a step-by-step explanation?
Related Questions:
- What is the domain of this function?
- How do you determine the slope of the line segment?
- Can this graph be extended to represent the entire real number line?
- How would the equation of the line segment be expressed in slope-intercept form?
- What is the midpoint of this line segment?
Tip:
For linear functions, the range is determined by observing the -values covered by the graph (line or segment). For infinite lines, the range is usually all real numbers, unless otherwise restricted.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Range of a Function
Graph Analysis
Formulas
Range is the set of all possible y-values for a function.
Theorems
Linear functions follow the general form y = mx + b.
Suitable Grade Level
Grades 6-8