Describe the domain and range of the graph of g (x) = 2 √x + 3.

Try this explanation:

1) Domain of the given function.

to define the domain of the function: sqrt (x) ≥0, ⇒ x≥0.

It means, the domain is x∈[0; +∝).

2) Range of the given function.

Property of this function: when the 'x' is the minimum value, then the 'g (x) ' has minimum value; when the 'x' is the maximum value, then the 'g (x) ' has maximum value. Using this property and the domain defined above, minimum of g (x) is 3 (the expression has '+3'!), maximum is + ∝.

It means, the range is g (x) ∈[3; +∝).