What is its Domain and Range.

Question

The equation is f(x)= |x- 2|.

Answer 1

For domain, it's sometimes easier to ask: What values can "x" not be? In this case, I can't think of any. Can you? So the domain is all real numbers, This can be written in several ways:

1. English words: All Real Numbers
2. Inequality: -∞ < x < ∞
3. Set Builder Notation: { x | -∞ < x < ∞ }
4. Interval Notation: (-∞, ∞)

The range is a little harder. What would be the smallest result of any number used as an input? Since the absolute value will make the result positive, the smallest result would come from x being equal to 2 and it is zero. So the range is all numbers greater than or equal to zero. Again, this can be written in several ways:

1. English words: All Numbers greater than or equal to zero
2. Inequality: 0 < y < ∞
3. Set Builder Notation: { y | 0 < y < ∞ }
4. Interval Notation: [0, ∞)