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:
- How can you determine the domain and range of a graph that is not a function?
- What are the different types of symmetry, and how do you test for them?
- Why does the vertical line test determine if a graph is a function?
- How do you find intercepts on a graph, and what do they represent?
- 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