Math Problem Statement

what is the domain of the function using interval notation

What is the domain of the function using interval notation?

Solution

The graph shows a function that spans horizontally from x=3x = -3 to x=5x = 5. The left endpoint at x=3x = -3 is an open circle, indicating that this point is not included in the domain. The right endpoint at x=5x = 5 is a closed circle, indicating that this point is included in the domain.

Thus, the domain of the function in interval notation is: (3,5](-3, 5]

Would you like further clarification or details on this solution?

Here are 5 related questions to deepen understanding:

  1. How is the domain of a function defined?
  2. What is the difference between open and closed intervals?
  3. How would the domain change if the open circle at x=3x = -3 were closed?
  4. What would the range of this function be, based on the graph?
  5. How can you find the domain of a more complex function algebraically?

Tip: Remember, an open circle means the value is not included, while a closed circle means the value is included in the domain or range.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Interval Notation

Formulas

-

Theorems

Open and Closed Intervals

Suitable Grade Level

Grades 8-10