Questions and Answers
What is the domain of the function in Card 1?
What is the range of the function in Card 2?
-2 < y < 6
The function in Card 3 is a function.
False
What is the range of the function in Card 4?
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The function in Card 5 has a domain of x > 0.
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What is the range of the function in Card 6?
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What is the domain of the function in Card 7?
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What is the range of the function in Card 8?
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The function in Card 9 is a function.
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What is the domain of the function in Card 10?
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Study Notes
Domain and Range Overview
- Understanding domain and range is crucial for determining the characteristics of functions in graphs.
- The domain refers to the set of possible x-values, while the range refers to the set of possible y-values.
Domain and Range Examples
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Card 1
Domain: -7 ≤ x < 5
Range: -3 ≤ y < 1
Indicates a valid function as it passes the vertical line test. -
Card 2
Domain: x = -5
Range: -2 < y < 6
Invalid function since all x-values are the same (not a function). -
Card 3
Domain: -4 ≤ x ≤ 4
Range: -4 ≤ y ≤ 4
Not classified as a function because multiple y-values correspond to a single x-value. -
Card 4
Domain: x ≥ 0
Range: All Real Numbers
This does not form a function; it has vertical line overlaps. -
Card 5
Domain: x > 0
Range: y = 4
Valid function, as there is a consistent y-value for all x-values in the domain. -
Card 6
Domain: -3 < x ≤ 5
Range: y = -1
It represents a valid function with a single y-value across the defined domain. -
Card 7
Domain: -4 ≤ x ≤ 2
Range: -2 ≤ y ≤ 4
This is a proper function indicating a one-to-one relationship within the specified range. -
Card 8
Domain: -3 < x < 4
Range: 0 ≤ y < 5
It qualifies as a function with bounded output values. -
Card 9
Domain: -3 ≤ x ≤ 4
Range: -2 ≤ y ≤ 4
Non-function due to multiple y-values being linked to specific x-values. -
Card 10
Domain: All Real Numbers
Range: y ≥ 0
Defines a valid function with a horizontal asymptote at y = 0.
Function Criteria
- A function must have only one output (y-value) for each input (x-value) to be valid.
- Graphically, a vertical line drawn through any part of the graph should intersect it at no more than one point.
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Description
This quiz explores the concepts of domain and range essential for analyzing functions in graphs. Through various examples, it identifies valid and invalid functions based on x and y values. Test your understanding of these crucial concepts and determine the characteristics of different functions.