the function $f(x)=5(\\frac{1}{5})^x$ is reflected over the y - axis. which equations represent the…

the function $f(x)=5(\\frac{1}{5})^x$ is reflected over the y - axis. which equations represent the reflected function? select two options.\n$\\square f(x)=\\frac{1}{5}(5)^{-x}$\n$\\square f(x)=\\frac{1}{5}\\frac{1}{5}(\\frac{1}{5})^x$\n$\\square f(x)=5(\\frac{1}{5})^{-x}$\n$\\square f(x)=5(5)^x$\n$\\square f(x)=5(5)^{-x}$

the function $f(x)=5(\\frac{1}{5})^x$ is reflected over the y - axis. which equations represent the reflected function? select two options.\n$\\square f(x)=\\frac{1}{5}(5)^{-x}$\n$\\square f(x)=\\frac{1}{5}\\frac{1}{5}(\\frac{1}{5})^x$\n$\\square f(x)=5(\\frac{1}{5})^{-x}$\n$\\square f(x)=5(5)^x$\n$\\square f(x)=5(5)^{-x}$

Answer

Answer:

C. $f(x)=5\left(\frac{1}{5}\right)^{-x}$, D. $f(x)=5(5)^{x}$

Explanation:

Step1: Recall reflection rule

When a function $y = f(x)$ is reflected over the $y$-axis, the transformation is $y=f(-x)$.

Step2: Apply to given function

Given $f(x)=5\left(\frac{1}{5}\right)^{x}$, then $f(-x)=5\left(\frac{1}{5}\right)^{-x}$.

Step3: Simplify the result

Using the exponent rule $a^{-n}=\frac{1}{a^{n}}$, we have $5\left(\frac{1}{5}\right)^{-x}=5\times5^{x}=5(5)^{x}$.