The function f(x) = |x – 2| is an absolute value function, which means it takes any input value (x), calculates the expression inside the absolute value bars, and returns the non-negative value of that expression.
In this case, we can break down the function:
- The expression inside the absolute value is (x – 2).
- This means that no matter what value you input for x, the result of |x – 2| will always be greater than or equal to zero because absolute values cannot be negative.
Now, let’s discuss the domain of this function:
- The domain of a function refers to all possible input values (x) for which the function is defined.
- For f(x) = |x – 2|, there are no restrictions on the values of x. You can substitute any real number into the function.
- Therefore, the domain of f(x) = |x – 2| is all real numbers.
In interval notation, we can express the domain as:
Domain: (-∞, ∞)
This means that you can input any number, whether it’s positive, negative, or zero, into the function without any issues. The absolute value function will always output a non-negative result based on the input provided.