Math Problem Statement

Determine the domain and range of the graph, which shows a straight line extending from (-8, -5) to (8, 7).

Solution

The image shows a straight line on a graph. To determine the domain and range of this line:

1. Domain: The domain refers to all possible x-values (horizontal axis) the graph covers.

  • The graph stretches from x=8x = -8 on the left to x=8x = 8 on the right.
  • Therefore, the domain is 8x8-8 \leq x \leq 8.

2. Range: The range refers to all possible y-values (vertical axis) the graph covers.

  • The graph extends vertically from y=5y = -5 at the bottom to y=7y = 7 at the top.
  • Hence, the range is 5y7-5 \leq y \leq 7.

Answer:

  • Domain: 8x8-8 \leq x \leq 8
  • Range: 5y7-5 \leq y \leq 7

Would you like more details or explanations?

Here are 5 related questions to extend your understanding:

  1. How can you identify the slope of a line from a graph like this?
  2. What would the equation of the line be in slope-intercept form?
  3. How do changes in the slope affect the domain and range of a line?
  4. How can you determine the intercepts of a line from a graph?
  5. How would the domain and range change if the line extended indefinitely?

Tip: Always check for any restrictions (like arrows) on the graph when determining the domain and range, as they might indicate the line extends beyond the visible area.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Functions
Linear Functions

Formulas

Domain and Range Definitions

Theorems

Linear Function Theorem

Suitable Grade Level

Grades 7-9