Math Problem Statement

Use the graph shown below. Write your answers in interval notation. Domain: _______ Range: _______

Solution

Based on the graph in the image, let's determine the domain and range of the function.

Domain:

The domain consists of all the x-values where the function is defined. From the graph:

  • The x-values range from -5 to 6 (inclusive), as the function exists between these points.

Thus, the domain is: Domain=[5,6]\text{Domain} = [-5, 6]

Range:

The range consists of all the y-values the function can take. From the graph:

  • The lowest y-value is -5, and the highest y-value is 5.

Thus, the range is: Range=[5,5]\text{Range} = [-5, 5]

You can now input:

  • Domain: [5,6][-5, 6]
  • Range: [5,5][-5, 5]

Would you like more details or have any questions?

Here are five related questions to explore:

  1. How do you determine the domain and range of a more complex graph?
  2. How would the domain and range change if there were open or closed dots on the graph?
  3. What happens to the domain and range when dealing with piecewise functions?
  4. Can you have a function with an infinite domain but a finite range?
  5. How do transformations like shifting or stretching affect the domain and range of a function?

Tip: Always look for any breaks or gaps in the graph when determining the domain and range.

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Math Problem Analysis

Mathematical Concepts

Domain and Range
Graph Analysis
Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9