Answer:
Graph C.
Domain: [-1, ∞)
Range: [0, ∞)
Step-by-step explanation:
When we have a function h(x) = f(x + c), we can say that the graph of h(x) is the graph of f(x) shifted c units to the left.
In this case, we have h(x) = √(x + 1), so, if the basic function is f(x) = √x, we can say that
h(x) = f(x + 1)
h(x) = √(x + 1)
Therefore, the graph of h(x) is the graph of y = √x shifted 1 unit to the left. So, the correct graph is C.
Then, the domain is the set of values that the variable x can take and the range is the set of values that h(x) can take. So, the domain and range of h(x) are
Domain: [-1, ∞)
Range: [0, ∞)