Answer:
The function f(x) = |x - 3| represents the absolute value of the expression (x - 3).
To understand what this means, let's break it down step by step:
1. The expression (x - 3) represents the difference between x and 3.
- For example, if x is 5, then (x - 3) would be (5 - 3) which equals 2.
2. The absolute value of a number is its distance from zero on the number line, ignoring the sign.
- For example, the absolute value of -2 is 2, because -2 is two units away from 0 on the number line.
3. So, when we apply the absolute value to the expression (x - 3), we are essentially taking the distance between (x - 3) and 0 on the number line, ignoring the sign.
4. If (x - 3) is positive or zero, then the absolute value of (x - 3) will be equal to (x - 3) itself.
- For example, if x is 5, then (x - 3) is 2, and the absolute value of (x - 3) would also be 2.
5. If (x - 3) is negative, then the absolute value of (x - 3) will be equal to -(x - 3), which is the opposite of (x - 3).
- For example, if x is 1, then (x - 3) is -2, and the absolute value of (x - 3) would be 2.
In summary, the function f(x) = |x - 3| will output the positive difference between x and 3.