Question

chris has a large collection of hockey cards and wants to get rid of some of his hockey cards. he gives 2 cards away on day 1, 4 cards away on day 2, and 8 cards away on day 3. he continues this pattern for 10 days. which statement describes why this sequence is a function? select each correct answer. the graph of this sequence would pass the vertical line test. each amount of hockey cards corresponds to a unique day in this sequence. each day corresponds to a unique amount of hockey cards in this sequence. the graph of this sequence would pass the horizontal line test.

Explanation:

To determine why the sequence is a function, we analyze each option:

1. Vertical Line Test: A function is defined such that for each input (day), there is exactly one output (cards given). The vertical line test checks if a graph represents a function (one input to one output), so if the graph passes it, it's a function. This is correct.
2. "Each amount...unique day": This is the reverse - a function requires each input (day) to have one output (cards), not each output to have one input. So this is incorrect.
3. "Each day...unique amount": For a function, each input (day) must map to exactly one output (cards given). Here, each day (input) has a unique number of cards (output), so this fits the function definition. Correct.
4. Horizontal Line Test: This tests for one - to - one functions (each output has one input), not just functions. The sequence being a function doesn't require passing the horizontal line test. Incorrect.

Answer:

• The graph of this sequence would pass the vertical line test.
• Each day corresponds to a unique amount of hockey cards in this sequence.