Question

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

Answer 1

Answer:

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