Math Problem Statement
domain and range of these graphs
Solution
To find the domain and range of the given graphs, let's analyze them:
Graph 4: Ellipse
The graph is an ellipse centered at the origin.
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Domain (x-values):
The ellipse spans horizontally from -2 to 2.
Domain: [-2, 2] -
Range (y-values):
The ellipse spans vertically from -3 to 3.
Range: [-3, 3]
Graph 7: Curve
The graph is a cubic-like curve.
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Domain (x-values):
The curve extends infinitely to the left and right, covering all real x-values.
Domain: (-∞, ∞) -
Range (y-values):
The curve rises and falls infinitely, covering all real y-values.
Range: (-∞, ∞)
Would you like further clarification on these points or additional examples?
Relative Questions:
- How are domain and range defined for general functions?
- Can a function's domain differ from its graph's visible extent?
- What is the significance of the center of an ellipse for determining its domain and range?
- How can you determine the domain and range of a polynomial function algebraically?
- What are some practical applications of domain and range in real-world scenarios?
Tip: Always check endpoints or asymptotes on graphs to determine domain and range accurately.
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Math Problem Analysis
Mathematical Concepts
Domain and Range
Graph Interpretation
Functions
Formulas
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Theorems
Definition of Domain and Range
Suitable Grade Level
Grades 9-12