Problem

Start with the graph of $f(x)=7^{x}$. Then write a function $g(x)$ that results from the given transformation. reflect $f(x)$ about the $x$-axis \[ g(x)=-6 x \]

Solution

Step 1 :The given function is \(f(x) = 7^{x}\).

Step 2 :We are asked to reflect this function about the x-axis.

Step 3 :A reflection about the x-axis changes the sign of the function, so the transformed function \(g(x)\) is \(-f(x)\).

Step 4 :Substituting \(f(x)\) into the equation gives \(g(x) = -7^{x}\).

Step 5 :So, the function \(g(x)\) that results from reflecting \(f(x) = 7^{x}\) about the x-axis is \(\boxed{g(x) = -7^{x}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/18450/

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