Here we want to find an equation for a function given that we know it is a transformation of the square root parent function and that it passes through the point (3, 8).
We will see that the new function can be: g(x) = √x + 9.732
We define a transformation of a function f(x) as an operator that, when applied to the function, changes it in some way. Some transformations will move the graph of f(x), some will shrink it, some will reflect it.
In this case, we know that we have:
f(x) = √x
And we apply a transformation to this, generating g(x), such that:
g(3) = 8.
Let's assume that the transformation is a vertical shift, this means that we just add a constant to f(x), so we get:
g(x) = f(x) + k
Using what we know, we can write:
g(3) = f(3) + k = 8
√3 + k = 8
k = 8 + √3 = 9.732
Then the new function can be:
g(x) = √x + 9.732
This represents a vertical shift of 9.732 units up, meaning that we "moved" the graph of f(x) by 9.732 units upwards.
If you want to learn more about transformations, you can read:
https://brainly.com/question/4289712
