Understanding the Function f(x) = |x – 3| – 1 | Step-by-Step Explanation and Examples

f(x) = |x – 3| – 1

Let’s break down the function f(x) = |x – 3| – 1 step by step:

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Let’s break down the function f(x) = |x – 3| – 1 step by step:

1. Absolute Value Function: The function |x – 3| represents the absolute value of the quantity (x – 3). The absolute value of a number is its distance from zero on the number line. For example, |4| = 4 because 4 is 4 units away from 0, and |-3| = 3 because -3 is 3 units away from 0.

2. Subtracting 1: The function subtracts 1 from the absolute value result. This means that whatever value |x – 3| gives, we subtract 1 from it. For example, if |x – 3| = 5, then f(x) = 5 – 1 = 4.

So, putting it all together, the function f(x) takes the absolute value of (x – 3) and then subtracts 1 from the result.

To better understand how this function affects different values of x, let’s consider a few examples:

1. When x = 2:
|2 – 3| – 1 = |-1| – 1 = 1 – 1 = 0
Therefore, f(2) = 0.

2. When x = 3:
|3 – 3| – 1 = |0| – 1 = 0 – 1 = -1
Therefore, f(3) = -1.

3. When x = 4:
|4 – 3| – 1 = |1| – 1 = 1 – 1 = 0
Therefore, f(4) = 0.

Note that for values of x less than 3, the function will always result in a negative value since |x – 3| will be negative. For values of x greater than 3, the function will always result in a positive value since |x – 3| will be positive.

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