Question

PLEASE HELPPPP

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.

Answer 1

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?

Answer 2

B , C

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.