Question

Chris has a large collection of hockey cards and wants to get of 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.


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

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

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

d. Each day corresponds to a unique amount of hockey cards in this sequence.

Answer 1

We define

day--------------------------X
hockey cards away ------------f(X)
He gives 2 cards away ----------------on day 1----------f(X)=2   X=1
He gives 4 cards away ----------------on day 2----------f(X)=4   X=2
He gives 8 cards away ----------------on day 3----------f(X)=8   X=3
the sequence of cards away      2,4,8,16,32,64,128,256,512,1024 

f(x) = 2**(x)

The answers are

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

Each element of the Domain (X = day), relates to a single value of f(x) = number of hockey cards

That is, every value of X must have only one corresponding value of f(x)
(One value of y, for each input X)

This can also be checked by using the vertical line test. 

If we plot f(x) and we draw vertical lines in the curve, we can verify that at every input the line intersects only one point of f(x)