what is the domain and range of the following equation

Question

f(x) = |x+2|

Answer 1

There are no domain restrictions on an absolute value, meaning that you can plug in any real number for the x-value and still produce a real number as an output. Knowing this, the domain of f(x) is all real numbers,

which can be written in interval notation as D: (-∞, ∞).

In interval notation, the "(" and ")" indicate non-inclusivity and the "[" and "]" indicate inclusivity. It is standard convention to use the parentheses for -∞ and ∞.

Now for the Range:

Remember, an absolute value causes negative numbers to become positive. Knowing this, any y-values less than 0 will now become positive and, therefore, greater than 0. This means that y ≥ 0 or that R: [0, ∞).

Hope this helped :)

Answer 2

Hi! The domain of the function is all real rumbers, ℜ, and as f(x) can never be negative the range is f(x) ≥ 0, or in interval notation [0, ∞).