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.

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:

  1. The line segment is located in the lower-right part of the graph.
  2. The segment begins at around x=5x = 5 and y=6y = -6 and ends near x=9x = 9 and y=8y = -8.
  3. As xx increases from 5 to 9, yy decreases linearly.

Range of the Function:

The range of the function corresponds to the set of all possible yy-values the graph covers. From the graph:

  • The lowest yy-value is -8 (at x=9x = 9).
  • The highest yy-value is -6 (at x=5x = 5).

Thus, the range of the function is:

8y6-8 \leq y \leq -6


Final Answer:

The range is 8y6-8 \leq y \leq -6.


Do you need further clarification or a step-by-step explanation?


Related Questions:

  1. What is the domain of this function?
  2. How do you determine the slope of the line segment?
  3. Can this graph be extended to represent the entire real number line?
  4. How would the equation of the line segment be expressed in slope-intercept form?
  5. What is the midpoint of this line segment?

Tip:

For linear functions, the range is determined by observing the yy-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