Questions and Answers
Is the following set a function? Domain: -7 ≤ x < 5, Range: -3 ≤ y < 1
Is the following set a function? Domain: x = -5, Range: -2 < y < 6
Is the following set a function? Domain: -4 ≤ x ≤ 4, Range: -4 ≤ y ≤ 4
Is the following set a function? Domain: x ≥ 0, Range: All Real Numbers
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Is the following set a function? Domain: x > 0, Range: y = 4
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Is the following set a function? Domain: -3 < x ≤ 5, Range: y = -1
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Is the following set a function? Domain: -4 ≤ x ≤ 2, Range: -2 ≤ y ≤ 4
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Is the following set a function? Domain: -3 < x < 4, Range: 0 ≤ y < 5
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Is the following set a function? Domain: -3 ≤ x ≤ 4, Range: -2 ≤ y ≤ 4
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Is the following set a function? Domain: All Real Numbers, Range: y ≥ 0
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Is the following set a function? Domain: All Real Numbers, Range: All Real Numbers
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Study Notes
Function Identification and Domain/Range Analysis
- A function is determined by evaluating if each input (x-value) has a unique output (y-value).
- If any x-value maps to multiple y-values, it is not a function.
Specific Cases of Functions
- Card 1: Function is valid; Domain: -7 ≤ x < 5; Range: -3 ≤ y < 1
- Card 2: Not a function; Domain: x = -5; Range: -2 < y < 6
- Card 3: Not a function; Domain: -4 ≤ x ≤ 4; Range: -4 ≤ y ≤ 4
- Card 4: Not a function; Domain: x ≥ 0; Range: All real numbers
- Card 5: Function is valid; Domain: x > 0; Range: y = 4 (constant function)
- Card 6: Function is valid; Domain: -3 < x ≤ 5; Range: y = -1 (constant function)
- Card 7: Function is valid; Domain: -4 ≤ x ≤ 2; Range: -2 ≤ y ≤ 4
- Card 8: Function is valid; Domain: -3 < x < 4; Range: 0 ≤ y < 5
- Card 9: Not a function; Domain: -3 ≤ x ≤ 4; Range: -2 ≤ y ≤ 4
- Card 10: Function is valid; Domain: All real numbers; Range: y ≥ 0
- Card 11: Function is valid; Domain: All real numbers; Range: All real numbers
Key Concepts
- Domain refers to the set of all possible x-values for which the function is defined.
- Range refers to the set of all possible y-values that the function can output.
- Constant functions have a fixed y-value across a range of x-values, as seen in Cards 5 and 6.
- Intervals in domain and range can be open (not inclusive) or closed (inclusive).
Studying That Suits You
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Description
Test your understanding of functions by determining if a graph represents a function, and identifying its domain and range. This quiz includes multiple examples to enhance your algebraic skills related to function analysis.