Answer:
Domain: (-∞, ∞)
Range: (-∞, ∞)
Explanation:
The parenting function of g(x) = (x + 3)³ + 5 is f(x) = x³.
The graph of f(x) = x³ is
Then, if we have a function g(x) = f(x + c), we can say that g(x) is the graph of f(x) shifted c units to the left and if we have a function g(x) = f(x) + c, we can say that g(x) is the graph of f(x) shifted c units up
In this case, g(x) = f(x + 3) + 5 because
g(x) = f(x + 3) + 5
g(x) = (x + 3)³ + 5
So, g(x) has the graph of f(x) shifted 3 units to the left and 5 units up.
Therefore, the graph of g(x) is
Now, the domain is the set of values that x can take and the range is the set of values that y can take, so the domain and range are all the real number.
Domain: (-∞, ∞)
Range: (-∞, ∞)
