how to write domian and range for a graph math

Answer 1

When writing the domain and range of a graph in mathematics, you are essentially identifying the set of possible input values (domain) and the set of possible output values (range). Here's how to do it:

1. Understand Domain and Range

• Domain: All the possible x-values (inputs) that the function can take.
• Range: All the possible y-values (outputs) that the function can produce.

2. Analyze the Graph

Steps to Determine Domain and Range from a Graph:

Identify the Domain:

• Vertical line test: Check for all x-values on the graph.
• Look for exclusions: Identify any points where the function is not defined, such as holes, vertical asymptotes, or values leading to undefined expressions (like division by zero).
• Write in interval notation: For continuous segments, use parentheses or brackets to denote whether endpoints are included.

Example of Domain:

• If the graph covers every x-value from -3 to 2 but does not include 1 (due to a hole), the domain is: \[ (-\infty, -3] \cup (-3, 1) \cup (1, 2] \cup (2, \infty) \]

Identify the Range:

• Horizontal line test: Check for all y-values on the graph.
• Look for exclusions: Like the domain, identify points (or horizontal asymptotes) where y-values are excluded.
• Write in interval notation: Similar to the domain, represent continuous segments appropriately.

Example of Range:

• If the graph covers all y-values from -2 to 5, but does not include -1 (due to a horizontal asymptote), the range is: \[ [-2, -1) \cup (-1, 5] \]

3. Graph Specifics:

• Closed intervals (e.g., [a, b]) indicate that the endpoints are included.
• Open intervals (e.g., (a, b)) indicate that the endpoints are not included.
• Infinity is always open (e.g., (a, ∞), or (-∞, b)).

4. Write the Results Clearly:

Clearly state both the domain and range, for example:

Domain: \( (-\infty, -3] \cup (-3, 1) \cup (1, 2] \cup (2, \infty) \)
Range: \( [-2, -1) \cup (-1, 5] \)

Additional Tips:

• Use a pencil to outline or highlight portions of the graph.
• If you're using a digital graphing tool, it might also indicate the domain and range.
• Make sure to check for any asymptotes or discontinuities that could affect the domain and range.

By following these steps, you can accurately determine and express the domain and range from a graph!