A piecewise-defined function is shown.

select the correct option mentioned below.
Statement 1: If the value of n changes, then the range of the function also changes.
Statement 2: If the value of n = 4, then the range is f(x) ≤ 2.

The correct answer is: Only statement 1 is correct

Step 1 of 2:
First, we check the statement 2 is correct or not.
Say, if n = 4.
f(1) = x – 1 = 1 – 1 = 0; f(2) = x – 1 = 2 – 1 = 1; f(3) = x – 1 = 3 – 1 = 2; f(4) = -x + 4 = -4 + 4 = 0; f(5) = -x + 4 = -5 + 4 = -1; f(6) = -x + 4 = -6 + 4 = -2 etc.
So, here the range is f(x) ≤ 2. Hence, statement 2 is correct.
Step 2 of 2:
If n = 7, then
f(1) = x - 1 = 1 - 1 = 0; f(2) = x - 1 = 2 - 1 = 1; f(3) = x - 1 = 3 - 1 = 2; f(4) = x - 1 = 4 - 1 = 3; f(5) = x - 1 = 5 - 1 = 4; f(6) = x - 1 = 6 - 1 = 5; f(7) = -x + 4 = -7 + 4 = -3; f(8) = -x + 4 = -8 + 4 = -4 etc.
So, here the range is f(x) ≤ 5.
That means changing the value of n changes the range. Hence, statement 1 is correct.
Final Answer:
The right choice is- c. Both statement 1 & statement 2 are correct.