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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

Write the rule for the function g(x)g(x) reflects f(x)=-1(x-4)^4 +1 across the x-axis-example-1
User DavidOhara
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Answer:
g(x)=x^4-4Step-by-step 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}

User Darko Rodic
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