Question

the table below shows some input and output values for a function named f(n). which of the following equations describes f(n)?

n	f(n)
1	8
2	11
5	20
10	35
20	65

a. f(n) = 3n + 5
b. f(n) = n + 5
c. f(n) = 4n

Explanation:

Step1: Test Option A

For \( n = 0 \): \( F(0)=3(0)+5 = 5 \), matches the table.
For \( n = 1 \): \( F(1)=3(1)+5 = 8 \), matches.
For \( n = 2 \): \( F(2)=3(2)+5 = 11 \), matches.
For \( n = 5 \): \( F(5)=3(5)+5 = 20 \), matches.
For \( n = 10 \): \( F(10)=3(10)+5 = 35 \), matches.
For \( n = 20 \): \( F(20)=3(20)+5 = 65 \), matches.

Step2: Test Option B

For \( n = 1 \): \( F(1)=1 + 5 = 6
eq 8 \), fails.

Step3: Test Option C

For \( n = 0 \): \( F(0)=4(0)=0
eq 5 \), fails.

Thus, only Option A satisfies all values.

Answer:

A. \( F(n) = 3n + 5 \)