Option C:
f(x) = 5x + 7 is the function of the input-output table.
Solution:
Option A: f(x) = 6x + 9
Input x = 1 in the above equation.
f(1) = 6(1) + 9
= 6 + 9
f(1) = 15
But the output is 12 in the table.
So, it is not the function of the table.
Option B: f(x) = 7x + 5
Input x = 1 in the above equation.
f(1) = 7(1) + 5
f(1) = 12
Input x = 5 in the above equation.
f(5) = 7(5) + 5
f(5) = 40
But the output is 32 in the table.
So, it is not the function of the table.
Option C: f(x) = 5x + 7
Input x = 1 in the above equation.
f(1) = 5(1) + 7
f(1) = 12
Input x = 5 in the above equation.
f(5) = 5(5) + 7
f(5) = 32
Input x = 10 in the above equation.
f(10) = 5(10) + 7
f(10) = 57
Input x = 5 in the above equation.
f(15) = 5(15) + 7
f(15) = 82
All outputs are correct for the given input.
Hence it is the function of the table.
Option D: f(x) = 12x + 1
Input x = 1 in the above equation.
f(1) = 12(1) + 1
f(1) = 12
Input x = 5 in the above equation.
f(5) = 12(5) + 1
f(5) = 61
But the output is 32 in the table.
So, it is not the function of the table.
Hence Option C is the correct answer.
f(x) = 5x + 7 is the function of the input-output table.