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?

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.

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

You need to show me the graphs so that i can choose one