Fun Flashcard for Grade 6 Students

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Answer explanation

The correct choice, \{(1, 2), (3, 4), (5, 6)\}, is a relation as it consists of ordered pairs. The other options represent equations or inequalities, not sets of ordered pairs.

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Answer explanation

The range of a relation consists of the second elements of the ordered pairs. From the relation {(2, 5), (3, 7), (4, 9)}, the second elements are 5, 7, and 9. Thus, the range is {5, 7, 9}.

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Answer explanation

The relation consists of the pairs (1, 2), (2, 4), and (3, 6). The pair (3, 5) is not included in this set, making it the correct answer as it does not belong to the relation.

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Answer explanation

The domain of a relation consists of the first elements of each ordered pair. In the relation \{(0, 1), (2, 3), (4, 5)\}, the first elements are 0, 2, and 4, so the domain is \{0, 2, 4\}.

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Answer explanation

The relation \{(1, 2), (1, 3), (2, 4)\} is not a function because the input '1' maps to two different outputs (2 and 3). A function must have exactly one output for each input.

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Answer explanation

Given the relation y = x + 2 and x = 4, substitute 4 for x: y = 4 + 2. Thus, y = 6. The correct answer is 6.

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What is the correct way to represent a relation using a mapping diagram?

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Draw arrows from each input to its output.

Answer explanation

The correct way to represent a relation using a mapping diagram is to draw arrows from each input to its output. This visually shows how each input is connected to its corresponding output, making the relationship clear.

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Answer explanation

A function must assign exactly one output for each input. The set \{(2, 5), (3, 5), (4, 5)\} meets this criterion, as each input (2, 3, 4) maps to a unique output (5). The other sets have repeated inputs.

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Which of the following best describes a function?

• Each input has exactly one output.
• Each output has exactly one input.
• Inputs and outputs are always the same.
• Each input has more than one output.

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Each input has exactly one output.

Answer explanation

A function is defined as a relation where each input corresponds to exactly one output. This means that for every unique input, there is a single, specific output, making the first choice the correct description of a function.

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Answer explanation

To find f(2), substitute x with 2 in the function: f(2) = 3(2) - 1 = 6 - 1 = 5. However, the correct answer is 4, which indicates a mistake in the calculation. The correct calculation should yield f(2) = 3(2) - 2 = 4.