Math Problem Statement

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

Solution

To solve the questions based on the given graphs, let's analyze each graph and determine if it represents a function, find its domain and range, intercepts, and symmetries.

Problem 10 (Top Graph)

Graph Analysis:

  • The graph has two loops, with one loop centered around the y-axis.

Determine if it is a function:

  • The vertical line test can be used to determine if a graph is a function. If a vertical line intersects the graph at more than one point, then it is not a function.
  • In this graph, a vertical line would intersect at multiple points, especially along the x-values where the loops are present.

Answer:

  • D) Not a function

Problem 11 (Bottom Graph)

Graph Analysis:

  • This graph is a circle centered at the origin with a radius of 7.

Determine if it is a function:

  • Again, using the vertical line test, a vertical line would intersect the circle at two points along many x-values. This means it is not a function.

Answer:

  • D) Not a function

If you have any questions or need further clarification, feel free to ask!

Additional Questions:

  1. How can you determine the domain and range of a graph that is not a function?
  2. What are the different types of symmetry, and how do you test for them?
  3. Why does the vertical line test determine if a graph is a function?
  4. How do you find intercepts on a graph, and what do they represent?
  5. Can a circle ever be considered a function? Why or why not?

Tip: To check if a graph is a function, always consider the vertical line test as your first step; if any vertical line crosses the graph more than once, it is not a function.

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Math Problem Analysis

Mathematical Concepts

Graphing
Functions
Symmetry
Domain and Range
Vertical Line Test

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12

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