Math Problem Statement

Give the domain and range of the function shown in the graph.

Solution

From the given graph:

Domain:

The domain of a function includes all possible xx-values for which the function is defined. From the graph, the function is defined for all x>2x > -2. Thus, the domain is: (2,)(-2, \infty)

Range:

The range of a function includes all possible yy-values that the function outputs. From the graph, the function outputs all values y>3y > -3. Thus, the range is: (3,)(-3, \infty)

Let me know if you need further explanation or clarification on this!

Follow-up Questions:

  1. What does it mean for a function to have a restricted domain or range?
  2. How can you determine the domain and range of more complex graphs?
  3. What are common characteristics of functions with vertical asymptotes?
  4. Can you explain the significance of the point where the function approaches but does not cross the axis?
  5. How do transformations (e.g., shifts) affect the domain and range of a function?

Tip: Always pay attention to the behavior near boundaries or asymptotes when determining domain and range.

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Math Problem Analysis

Mathematical Concepts

Domain and Range
Functions
Graph Analysis

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10