Question

the function f is defined as follows.
$f(x)=3x^{2}+3$
if the graph of f is translated vertically upward by 7 units, it becomes the graph of a function g.
find the expression for $g(x)$.
note that the aleks graphing calculator may be helpful in checking your answer.
$g(x) = \square$

Explanation:

Step1: Recall vertical translation rule

For a function \( y = f(x) \), a vertical upward translation by \( k \) units gives \( y = f(x)+k \). Here, \( k = 7 \) and \( f(x)=3x^{2}+3 \).

Step2: Apply the translation to \( f(x) \)

To find \( g(x) \), we add 7 to \( f(x) \). So, \( g(x)=f(x) + 7=(3x^{2}+3)+7 \).

Step3: Simplify the expression

Simplify \( (3x^{2}+3)+7 \) by combining like terms. \( 3 + 7 = 10 \), so \( g(x)=3x^{2}+10 \).

Answer:

\( g(x)=3x^{2}+10 \)