Math Problem Statement

Write the domain and range of each function using interval notation.

Solution

Let's analyze the two graphs to determine their domain and range using interval notation.

Graph A:

  • Domain: The domain is the set of all xx-values for which the function is defined.

    • The graph starts at x=8x = -8 and ends at x=6x = 6. Both points are solid, meaning they are included.
    • Domain: [8,6][ -8, 6 ]
  • Range: The range is the set of all yy-values that the function takes.

    • The graph covers yy-values from 8-8 to 1010. Both points are included in the range.
    • Range: [8,10][ -8, 10 ]

Graph B:

  • Domain: The domain for this graph includes all xx-values where the function exists.

    • The graph starts at x=10x = -10 and ends around x=8x = 8. However, there is an open circle at x=6x = -6, indicating that this value is not included.
    • Domain: (10,6)(6,8]( -10, -6 ) \cup ( -6, 8 ]
  • Range: The range represents all the yy-values the function takes.

    • The lowest value appears to be y=10y = -10 and goes upwards without bounds, though there is a gap around y=4y = -4 due to the open circle.
    • Range: [10,4)(4,)[ -10, -4 ) \cup ( -4, \infty )

Final Answer:

  • Graph A:

    • Domain: [8,6][ -8, 6 ]
    • Range: [8,10][ -8, 10 ]
  • Graph B:

    • Domain: (10,6)(6,8]( -10, -6 ) \cup ( -6, 8 ]
    • Range: [10,4)(4,)[ -10, -4 ) \cup ( -4, \infty )

Let me know if you'd like further details or have any questions.

Related Questions:

  1. How does the open or closed circle affect the domain and range of a function?
  2. What are the general steps for finding the domain and range of a function graphically?
  3. Can a function have an unbounded domain or range? How would it be represented?
  4. What does it mean when part of a graph has a break, such as in Graph B?
  5. How do you determine the domain of a composite function graphically?

Tip:

When analyzing a function graph, always pay attention to open and closed circles. Closed circles indicate the inclusion of that point, while open circles mean the point is excluded from the domain or range.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12