Question

Write the rule for the function g(x)g(x) reflects f(x)=-1(x-4)^4 +1 across the x-axis and translates 4 units left

Answer 1

Answer:$g(x)=x^4-4$Explanation:

The given function is:

$f(x)=-(x-4)^4+1$

To reflect across the x-axis:

y = -1

$\begin{gathered} f^{\prime}(x)=-[-(x-4)^4+1] \\ \\ f^{\prime}(x)=(x-4)^4-4 \end{gathered}$

Translate by 4 units left, you add 4 to x

$\begin{gathered} g(x)\text{ = \lparen x+4-4\rparen}^4-4 \\ \\ g(x)=x^4-4 \end{gathered}$