Math Problem Statement

El gráfico de la relación T se muestra a continuación. Indicar el dominio y el rango de T. Escribir las respuestas en notación conjuntista.

Solution

The image shows a graph of a relation, and you're asked to determine the domain and range of the relation in set notation.

To find the domain:

  • The domain consists of all the possible values of xx (the horizontal axis) where the relation is defined.
  • From the graph, the points appear to be at x=3x = -3, x=1x = -1, and x=2x = 2, so the domain is: dominio={3,1,2}\text{dominio} = \{-3, -1, 2\}

To find the range:

  • The range consists of all the possible values of yy (the vertical axis) corresponding to those xx-values.
  • From the graph, the points are at y=3y = 3, y=2y = -2, and y=4y = -4, so the range is: rango={3,2,4}\text{rango} = \{3, -2, -4\}

Would you like a more detailed explanation, or do you have any questions about how these sets are determined? Let me know!

Here are some related questions you could explore:

  1. How do you differentiate between functions and relations based on their graphs?
  2. What is the difference between set notation and interval notation?
  3. How can you determine if a relation is a function from its graph?
  4. How do vertical lines help in determining if a graph represents a function?
  5. What is the significance of having multiple yy-values for one xx-value?

Tip: Always check if any vertical lines drawn through the graph intersect it at more than one point. If they do, it means the graph is not a function.

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Math Problem Analysis

Mathematical Concepts

Funciones
Relaciones
Dominio
Rango

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9