Final answer:
Compared to the graph of the base function f(x)=√x, the graph of the function g(x)+8=√x is translated 8 units up. This is a vertical translation of the original function.
Step-by-step explanation:
The base function f(x) = √x represents the square root of x. When you compare this with the function g(x) + 8 = √x, you notice that there has been a transformation applied to the base function.
Specifically, the entire graph of f(x) has been moved in a way such that y gets increased by 8 units at every x. This type of transformation is known as a vertical translation.
Therefore, the correct answer to how the graph of g(x) is translated compared to the graph of the base function is option A: 8 units up.
To generalize further, if you have a function f(x) = √x and you add a constant to the function, resulting in f(x) = √x + c where c is a constant, the graph of the function is translated c units vertically upwards if c is positive, and c units downwards if c is negative.