Question

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 $g(x)$?\
\bigcirc $g(x) = (x + 9)^2 + 4$\
\bigcirc $g(x) = (x + 9)^2 - 4$\
\bigcirc $g(x) = (x - 4)^2 + 9$\
\bigcirc $g(x) = (x + 4)^2 + 9$

Explanation:

Step1: Recall Translation Rules

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

Step2: Apply to \( f(x)=x^2 \)

Here, \( h = 4 \) (right 4 units) and \( k = 9 \) (up 9 units). So substitute into the rule: \( g(x)=f(x - 4)+9=(x - 4)^2+9 \).

Answer:

\( g(x) = (x - 4)^2 + 9 \) (the third option)