Math Problem Statement

Find the domain and range of the function shown.

Solution

Domain and Range of the Function:

  1. Domain: The domain represents all the possible input values (x-values) for the function.

    • The graph starts from the left at x=2x = -2 (indicated by the open circle), meaning this point is not included in the domain.
    • The graph continues until x=1x = 1 (indicated by the closed circle), meaning this point is included in the domain.

    Therefore, the domain is:
    (2,1](-2, 1]

  2. Range: The range represents all the possible output values (y-values) for the function.

    • The highest point on the graph is around y=2y = 2, which is not included (open circle).
    • The lowest point on the graph is y=1y = -1, which is included (closed circle).

    Therefore, the range is:
    (1,2)(-1, 2)

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you find the domain and range of a function algebraically?
  2. What is the difference between open and closed intervals in domain and range?
  3. How do you determine if a function is continuous based on its graph?
  4. How can you identify whether a function is increasing or decreasing from a graph?
  5. What is the significance of the domain and range in real-world applications?

Tip: When determining the domain and range of a function from a graph, always pay attention to open and closed circles, as they indicate whether specific values are included or not.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Domain and Range
Functions
Graph Analysis

Formulas

-

Theorems

Understanding Open and Closed Intervals

Suitable Grade Level

Grades 9-11