Math Problem Statement

What is the DOMAIN of the function graphed?

Solution

To determine the domain of the function shown in the graph:

  1. Domain refers to the set of all possible x-values for which the function is defined.
  2. The graph has two endpoints:
    • The left endpoint at x=4x = -4, marked with an open circle, meaning x=4x = -4 is not included.
    • The right endpoint at x=8x = 8, marked with a solid circle, meaning x=8x = 8 is included.
  3. Between these two endpoints, the graph is a straight line, indicating the function is defined for all xx-values in that range.

Domain in interval notation:

(4,8](-4, 8]

  • The parenthesis on 4-4 indicates 4-4 is not included.
  • The bracket on 88 indicates 88 is included.

Would you like me to explain why this domain is restricted or go into more detail? Let me know if you need help with any other aspect of this graph!

Related Questions:

  1. What is the range of the function graphed?
  2. How do you write the domain and range of a graph with different types of endpoints?
  3. What is the slope of the line between the two points?
  4. How do you identify open and closed circles on a graph?
  5. How do you determine whether a function is continuous or not?

Tip:

In interval notation, always use parentheses ()() for values not included (open circles) and brackets [][] for included values (solid circles).

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Math Problem Analysis

Mathematical Concepts

Domain of a function
Interval Notation
Graph interpretation

Formulas

Domain: All x-values where the function is defined

Theorems

Open and Closed Interval Rules

Suitable Grade Level

Grades 9-11