Question

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

Answer 1

Domain = `[-4,oo)`
Range = `[0,oo)`

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 `[0,oo)`

The graph verifies this as well :

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