Explanation
From the graph, we see that the graph of G(x) is the graph of F(x) translated:
• 4 units to the left,
,
• 1 unit upward.
To translate the graph of F(x) a units to the right and b units upward, we apply the transformation:
[tex]F(x)\rightarrow G(x)=F(x-a)+b.[/tex]
In our case, we have:
• F(x) = x²,
,
• a = -4 (because the translation is 4 units to the left),
,
• b = 1.
Replacing these data in the formula above, we find that the equation of G(x) is:
[tex]G(x)=(x+4)^2+1.[/tex]Answer
B. G(x) = (x + 4)² + 1
