Algebra 1-Domain and Range Flashcards

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).