Math Problem Statement

domain and range of these graphs

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.

  • 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.

  • 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:

  1. How are domain and range defined for general functions?
  2. Can a function's domain differ from its graph's visible extent?
  3. What is the significance of the center of an ellipse for determining its domain and range?
  4. How can you determine the domain and range of a polynomial function algebraically?
  5. 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

-

Theorems

Definition of Domain and Range

Suitable Grade Level

Grades 9-12