For this case, the parent function is given by:
[tex] f (x) = x ^ 2
[/tex]
We apply the following transformations:
Vertical translations:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units upwards:
For k = 9 we have:
[tex] h (x) = x ^ 2 + 9
[/tex]
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right
For h = 4 we have:
[tex] g (x) = (x-4) ^ 2 + 9
[/tex]
Answer:
The function g (x) is given by:
[tex] g (x) = (x-4) ^ 2 + 9 [/tex]
