# What is the domain and range of y=abs(x+4)?

Domain: all real numbers; Range: $\left[0 , \infty\right)$
The absolute value of every real number is a (non-negative) real number. Therefore the domain is $\left(- \infty , \infty\right)$.
The range of y = x + 4 would be $\left(- \infty , \infty\right)$, but the absolute value makes all negative values positive. $| x + 4 |$ is smallest where x + 4 = 0. That is, when $x = - 4$. It attains all positive values. These positive values, k, would be solutions to the absolute value equation $| x + 4 | = k$. The range is $\left[0 , \infty\right)$ -- all positive values and zero.