Answer:
[tex]g(x) = (x - 2)^2 + 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
Required
Determine g(x)
f(x) represents the parent function. And from the graph, we have:
[tex]f(x) = x^2[/tex]
f(x) is first shifted 2 units right.
The rule is:
[tex]f'(x) = f(x - 2)[/tex]
So, we have:
[tex]f'(x) = (x - 2)^2[/tex]
Next, f'(x) is shifted 1 unit up to give g(x), the blue graph.
The rule to this is:
[tex]g(x) = f'(x) + 1[/tex]
[tex]g(x) = (x - 2)^2 + 1[/tex]
