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Thomas starts a canned food collection with two cans of food. He challenges his friends to bring 4 cans on the second day, 8 cans on the third day, and 16 cans on the fourth day. Thomas and his friends plan to collect cans for 10 days. Which statement describes why this sequence is a function? THERE CAN BE MORE THAN ONE ANSWER.

A.

Each amount of cans corresponds to a unique day in this sequence.

B.

The graph of the sequence would pass the vertical line test.

C.

Each day corresponds to a unique amount of cans in this sequence.

D.

The graph of the sequence would pass the horizontal line test.

B and C. The definition of a function says that for each value of x (day) there can be no more than one value of y (cans). A graph of a function passes the vertical line test when a vertical line touches no more than one point (which means it follows the first rule). Anything unclear?

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SerenaBochenek SerenaBochenek · Answer 2 · 2019-01-04T01:20:17-05:00

Answer:

B , C

Step-by-step explanation:

We assume that Thomas asked only one friend to participate.

It can be seen that the pattern for days and cans is as follows,

On the 1st day, Thomas has 2 cans i.e. \(2^{1}\) cans.

On the 2nd day, Thomas has 4 cans i.e. \(2^{2}\) cans.

On the 3rd day, Thomas has 8 cans i.e. \(2^{3}\) cans.

On the 4th day, Thomas has 16 cans i.e. \(2^{4}\) cans.

This pattern goes on till day 10.

So, we get on x day, Thomas has \(2^{x}\) cans , where x ranges from 1 to 10.

Therefore, the corresponding function is \(f(x)=2^{x}\).

This gives that for each day (x) there is a unique value of the amount of cans \((2^{x})\)

Now, the 'Vertical Line Test' is the test where we draw a vertical line passing through the graph and if it cuts the graph at exactly one point, then the graphed curve is a function.

As, we can see from the graph below, the vertical line cuts f(x) at exactly one point. Therefore, f(x) is a function.

Hence, 'the graph of the sequence passes the vertical line test.

Moreover, it is clear that 'each day corresponds to a unique amount of cans'.

Hence, options B and C are correct.