Math Problem Statement

The graph of the relation G is shown below. Give the domain and range of G.

Solution

Let's analyze the graph to determine the domain and range of the relation GG.

  1. Domain: The domain consists of all the xx-coordinates of the points on the graph. Looking at the points on the graph, the xx-coordinates are:

    • x=2x = -2
    • x=0x = 0
    • x=3x = 3
    • x=4x = 4

    So, the domain is: Domain={2,0,3,4}\text{Domain} = \{-2, 0, 3, 4\}

  2. Range: The range consists of all the yy-coordinates of the points on the graph. The yy-coordinates are:

    • y=4y = -4
    • y=2y = -2
    • y=1y = 1
    • y=4y = 4

    So, the range is: Range={4,2,1,4}\text{Range} = \{-4, -2, 1, 4\}

Thus, the domain and range of the relation GG are: Domain={2,0,3,4}\text{Domain} = \{-2, 0, 3, 4\} Range={4,2,1,4}\text{Range} = \{-4, -2, 1, 4\}

Would you like further clarification on this, or should I provide additional details?

Here are five related questions to expand on this topic:

  1. What is the difference between the domain and range of a function?
  2. Can a relation have the same xx-value mapped to multiple yy-values?
  3. How do we determine if a relation is a function from its graph?
  4. How does the range change if we reflect the graph across the xx-axis?
  5. What is the domain and range for common functions like f(x)=x2f(x) = x^2 or f(x)=sin(x)f(x) = \sin(x)?

Tip: When identifying the domain and range from a graph, always check the extent of the points on both the xx-axis and the yy-axis for a clear set of values.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Functions

Formulas

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Theorems

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Suitable Grade Level

High School