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 , 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. cans.

On the 2nd day, Thomas has 4 cans i.e. cans.

On the 3rd day, Thomas has 8 cans i.e. cans.

On the 4th day, Thomas has 16 cans i.e. cans.

This pattern goes on till day 10.

So, we get on x day, Thomas has cans , where x ranges from 1 to 10.

Therefore, the corresponding function is .

This gives that for each day (x) there is a unique value of the amount of cans

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.

d

step-by-step explanation: