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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

User Mamie
by
6.6k points

1 Answer

1 vote

Answer:

Option c:


f(n)=4n+1

Explanation:

The functional relationship between two variables can be easily found if it's represented as a line.

Larry's online calculator collects these points

(1, 5), (2, 9), (3, 13), (4, 17)

We can see there is a linear relation because every time the first component increases by 1, the second increases by 4.

The equation of a line is given by


f(n)=m.n+b

Where m is the slope of the line and can be computed as


\displaystyle m=(d-b)/(c-a)

Where (a,b), (c,d) are two known points of the line. Let's use the first two points (1, 5), (2, 9)


\displaystyle m=(9-5)/(2-1)=4

We now know that


f(n)=4n+b

To compute the value of b, we use one of the points again, for example (1,5):


5=4(1)+b => b=1

The relation is


f(n)=4n+1

We can test our results by using other points like (3,13)


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

And also


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

All points belong to the same function or rule


f(n)=4n+1

User Pschang
by
6.5k points