Math Problem Statement

Write the domain and range of the function using interval notation based on the provided graph.

Solution

Looking at the graph provided, we are tasked with determining the domain and range of the function shown.

Domain:

The domain refers to all the possible xx-values for which the function is defined. From the graph:

  • The graph starts around x=3x = -3 (with a closed point indicating it includes this value) and ends at x=2x = 2.
  • Therefore, the domain in interval notation is:
    [3,2][-3, 2]

Range:

The range refers to all the possible yy-values the function can take. From the graph:

  • The lowest yy-value is approximately 8-8, and the highest value is 22, which is included.
  • Therefore, the range in interval notation is: [8,2][-8, 2]

Summary:

  • Domain: [3,2][-3, 2]
  • Range: [8,2][-8, 2]

Let me know if you'd like further clarifications or more details!

Here are 5 related questions to expand your understanding:

  1. How do we determine if a point is included or excluded in the domain and range?
  2. What is the difference between open and closed intervals in interval notation?
  3. How can we describe the behavior of a function graphically when it includes or excludes certain points?
  4. Can a function have more than one range for a given domain?
  5. How do you describe the behavior of the graph if it has discontinuities or gaps?

Tip: When identifying the domain, always check the x-values covered by the graph from left to right, and for the range, focus on the y-values from bottom to top.

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
Interval Notation

Formulas

-

Theorems

Concept of Domain
Concept of Range

Suitable Grade Level

Grades 9-12