Question

the function g is defined as follows.
g(x)=3x² - 1
if the graph of g is translated vertically upward by 6 units, it becomes the graph of a function f.
find the expression for f(x).
f(x) =

Explanation:

Step1: Recall vertical translation rule

For a function $y = g(x)$, a vertical translation upward by $k$ units gives $y = g(x)+k$.

Step2: Apply the rule to $g(x)$

Given $g(x)=3x^2 - 1$ and $k = 6$ (upward translation), so $f(x)=g(x)+6$.
Substitute $g(x)$: $f(x)=(3x^2 - 1)+6$.

Step3: Simplify the expression

Simplify $(3x^2 - 1)+6$: $3x^2+(-1 + 6)=3x^2+5$.

Answer:

$f(x) = 3x^2 + 5$