# How do you find the domain and range of f(x)=sqrt(x+4)?

Oct 23, 2015

Domain = $\left[- 4 , \infty\right)$
Range = $\left[0 , \infty\right)$

#### Explanation:

The domain is all allowed x values and excludes values that either lead to division by zero or taking even square roots of negative numbers.

Clearly in this case hence the domain is all real x values greater than or equal to -4.,
that is Dom_f=[-4;oo)

The corresponding range is then all the possible y values allowed as outputs and is clearly $\left[0 , \infty\right)$

The graph verifies this as well :

graph{sqrt(x+4) [-11.97, 33.66, -9.85, 12.95]}