Math Problem Statement

What is the range of the function based on the graph of a linear function?

Solution

To find the range of the linear function, let's analyze the graph you provided.

The graph shows a line that is part of a linear function. The key point to note is that the line is moving downwards from left to right, which indicates a negative slope. Since it's a linear function, the line will continue indefinitely in both directions.

In a linear function like this, the range represents all possible yy-values that the function can take. Since the line extends infinitely in both upward and downward directions along the y-axis, the range of this function is:

(,)\boxed{(-\infty, \infty)}

In other words, the line will cover all real numbers for the yy-values.

Would you like more details or have any other questions?

Here are some related questions:

  1. How do we find the slope of the line from the graph?
  2. How would you write the equation of this line?
  3. What is the domain of a linear function?
  4. What happens if the line is vertical—how does that change the range?
  5. Can a linear function ever have a limited range?

Tip: For any linear function, unless the line is horizontal, the range will always be all real numbers (,)(-\infty, \infty).

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Range of a Function

Formulas

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Theorems

A linear function's range typically covers all real numbers unless the line is horizontal.

Suitable Grade Level

Grades 9-10