Given:
[tex]f(x)=\sqrt{x}[/tex]
Given the table:
x f(x)
0 0
1 1
4 2
9 3
16 4
Let's write a rule y = f(x) using the table after a transformation of the parent function.
Now, for the graph of the transformed function, we can produce the table, of values:
x g(x)
0 4
1 5
4 6
Now, let's compare both tables:
when x = 0; f(x) = 0, g(x) = f(x) + 4 = 0 + 4 = 4
when x = 1; f(x) = 1, g(x) = f(x) + 4 = 1 + 4 = 5
When x = 4; f(x) = 2, g(x) = f(x) + 4 = 2 + 4 = 6
This means there was a vertical translation 4 units up.
Therefore, the basic function that for the transformation will be: y = f(x) + 4
[tex]f(x)=\sqrt{x}+4[/tex]
ANSWER:
[tex]f(x)=\sqrt{x}+4[/tex]
