Larry is using an online calculator to calculate the outputs f (n) for different inputs n. The ordered pairs below show Larry's inputs and the corresponding outputs displayed by the calculator: (1, 5), (2, 9), (3, 13), (4, 17) Which of the following functions best represents the rule that the calculator uses to display the outputs? a. f (n) = 5n - 1 b. f (n) = 5n + 1 c. f (n) = 4n + 1 d. f (n) = 4n - 1

The answer is c. f (n) = 4n+1

Step-by-step explanation:

In the function of the answers, n is the input and f (n) is the output. So the ordered pairs needs to be at the form (n, f (n))

Additionally, in the ordered pairs given in the question, the first term is the input and the second term is the output. For example in the ordered pair (1,5), 1 is the input and 5 is the output.

So, if we replace n by 1, f (n) needs to be 5. This condition is only satisfied on option c. That's is also prove for every ordered pair as:

For (1,5)

if n=1 then:

f (n) = (4*1) + 1=5

For (2,9)

if n=2 then:

f (n) = (4*2) + 1=9

For (3,13)

if n=3 then:

f (n) = (4*3) + 1=13

For (4,17)

if n=4 then:

f (n) = (4*4) + 1=17

Finally, the functions that best represents the rule that the calculator uses to display the outputs is f (n) = 4n+1