Math Problem Statement

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

Solution

Let's analyze the graph to determine the domain and range in interval notation.

  1. Domain (x-values):

    • The graph starts at x=6x = -6 and continues to the right towards infinity.
    • Therefore, the domain is: [6,)[-6, \infty)
  2. Range (y-values):

    • The y-values start at y=0y = 0 and increase as the function goes up.
    • The range is: [0,)[0, \infty)

So, the answer is:

  • Domain: [6,)[-6, \infty)
  • Range: [0,)[0, \infty)

Would you like more details on how interval notation is applied here or have other questions?

Here are five additional questions that could help you explore further:

  1. How does interval notation represent open and closed intervals?
  2. What is the significance of including or excluding endpoints in interval notation?
  3. How can you determine the domain and range of different types of functions?
  4. How does domain and range change when transformations are applied to functions?
  5. How would the domain and range look for a function that decreases to negative infinity?

Tip: In interval notation, brackets [ ][ \ ] indicate that an endpoint is included (closed interval), while parentheses (( \ )) indicate that it is excluded (open interval).

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Math Problem Analysis

Mathematical Concepts

Domain and Range
Interval Notation
Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10