the function ( f(x)=x^{2} ) has been translated 9 units up and 4 units to the right to form the function (…

the function ( f(x)=x^{2} ) has been translated 9 units up and 4 units to the right to form the function ( g(x) ). which represents ( g(x) )?\n( g(x)=(x + 9)^{2}+4 )\n( g(x)=(x + 9)^{2}-4 )\n( g(x)=(x - 4)^{2}+9 )\n( g(x)=(x + 4)^{2}+9 )

the function ( f(x)=x^{2} ) has been translated 9 units up and 4 units to the right to form the function ( g(x) ). which represents ( g(x) )?\n( g(x)=(x + 9)^{2}+4 )\n( g(x)=(x + 9)^{2}-4 )\n( g(x)=(x - 4)^{2}+9 )\n( g(x)=(x + 4)^{2}+9 )

Answer

Explanation:

Step1: Recall the rules of function translation

For a function (y = f(x)), translating (h) units to the right gives (y = f(x - h)), and translating (k) units up gives (y=f(x)+k).

Step2: Apply the translation rules to (f(x)=x^{2})

Since the function is translated 4 units to the right, we replace (x) with (x - 4) in (f(x)), getting (y=(x - 4)^{2}). Then, since it is translated 9 units up, we add 9 to the function. So (g(x)=(x - 4)^{2}+9).

Answer:

C. (g(x)=(x - 4)^{2}+9)