Math Problem Statement
Which relation is a function?
Responses
Coordinate grid with unlabeled points at begin ordered pair negative two comma negative two end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma one end ordered pair and begin ordered pair two comma zero end ordered pair and begin ordered pair two comma negative two end ordered pair. Image with alt text: Coordinate grid with unlabeled points at begin ordered pair negative two comma negative two end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma one end ordered pair and begin ordered pair two comma zero end ordered pair and begin ordered pair two comma negative two end ordered pair.
Coordinate grid with unlabeled points at begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma two end ordered pair and begin ordered pair zero comma negative one end ordered pair and begin ordered pair one comma three end ordered pair and begin ordered pair two comma one end ordered pair
Image with alt text: Coordinate grid with unlabeled points at begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma two end ordered pair and begin ordered pair zero comma negative one end ordered pair and begin ordered pair one comma three end ordered pair and begin ordered pair two comma one end ordered pair
Coordinate grid with unlabeled points at begin ordered pair negative one comma negative one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair negative four comma three end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair one comma one end ordered pair and begin ordered pair two comma negative one end ordered pair Image with alt text: Coordinate grid with unlabeled points at begin ordered pair negative one comma negative one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair negative four comma three end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair one comma one end ordered pair and begin ordered pair two comma negative one end ordered pair
Coordinate grid with unlabeled points at begin ordered pair negative two comma zero end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma two end ordered pair and begin ordered pair one comma negative one end ordered pair and begin ordered pair two comma zero end ordered pair and begin ordered pair three comma two
Solution
In order to determine which of the relations is a function, we need to use the definition of a function. A relation is a function if each input (or x-coordinate) has exactly one output (or y-coordinate). This is often verified using the Vertical Line Test, which states that if a vertical line crosses the graph of the relation at more than one point, the relation is not a function.
Let's analyze the coordinate grids one by one:
1. First Grid
The points are: (-2, -2), (-2, 1), (-1, 3), (0, 1), (2, 0), (2, -2).
- The x-coordinate -2 appears twice with different y-values (-2, 1), and 2 appears twice with different y-values (0, -2).
- Since one x-value corresponds to more than one y-value, this is not a function.
2. Second Grid
The points are: (-2, 1), (-1, 3), (0, 2), (0, -1), (1, 3), (2, 1).
- The x-coordinate 0 appears twice with different y-values (2, -1).
- Since one x-value corresponds to more than one y-value, this is not a function.
3. Third Grid
The points are: (-1, -1), (-1, 3), (-4, 3), (-2, 1), (1, 1), (2, -1).
- The x-coordinate -1 appears twice with different y-values (-1, 3).
- Since one x-value corresponds to more than one y-value, this is not a function.
4. Fourth Grid
The points are: (-2, 0), (-1, 3), (0, 2), (1, -1), (2, 0), (3, 2).
- Each x-coordinate appears only once with one corresponding y-value.
- Since each x-value has only one y-value, this is a function.
Conclusion:
The fourth relation is a function because each x-coordinate has a unique corresponding y-coordinate.
Would you like further details or explanations on this topic?
Here are some related questions you might find helpful:
- What is the Vertical Line Test and how does it work?
- How can we represent relations using tables or mappings?
- What are some examples of real-life functions?
- Can a relation have multiple outputs for the same input and still be a function?
- How do you distinguish between functions and non-functions graphically?
Tip: When analyzing relations, always check if any x-value repeats with different y-values; if it does, the relation is not a function.
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Coordinate Geometry
Vertical Line Test
Formulas
-
Theorems
Vertical Line Test
Suitable Grade Level
Grades 8-10
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