Question

reflect the function $f(x)=x^4$ about the $x$-axis and translate it 3 units to the left to produce $g(x)$. which equation function $g(x)$?\
\\(\bigcirc\\) a $g(x)=-x^4 + 3$\
\\(\bigcirc\\) b $g(x)=-(x - 3)^4$\
\\(\bigcirc\\) c $g(x)=-x^4 - 3$\
\\(\bigcirc\\) d $g(x)=-(x + 3)^4$

Explanation:

Step1: Reflect over x-axis

To reflect $f(x)$ over the x-axis, multiply the function by $-1$:
$h(x) = -f(x) = -x^4$

Step2: Translate left 3 units

To translate a function left by $a$ units, replace $x$ with $x+a$. Here $a=3$:
$g(x) = h(x+3) = -(x+3)^4$

Answer:

D. $g(x) = -(x+3)^4$