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:

  1. The line begins at y=6y = 6 when x=6x = -6, and this point is marked with an open circle, meaning yy does not equal 6 at x=6x = -6.
  2. The line decreases and ends at a point on the y-axis with y=6y = -6 when x=8x = 8, marked with an arrow, which indicates that yy continues to decrease as xx moves right.

Therefore, the range of yy values is from 6-6 upward to just below 66. Thus:

  • Range: y5y \leq 5.

Would you like more details or have any questions?


Here are some follow-up questions to deepen understanding:

  1. How can we determine the slope of the line from the graph?
  2. What would the range be if the line extended infinitely in both directions?
  3. How would an open versus closed endpoint affect the range?
  4. How would the range change if the line had a positive slope?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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