Question

Which function represents g(x), a reflection of f(x)=4(1/2)^x across the x-axis?

Answer 1

Answer:

$g(x)=-4(\frac{1}{2})^x$

Step-by-step explanation:

Given:

The parent function is given as:

$f(x)=4(\frac{1}{2})^x$

The function $g(x)$ is a reflection of the parent function about the x-axis.

Now, in order to find the function g(x), we need to use the rules of function transformations.

As per transformation rules, when a function is reflected about the x-axis, the function rule is given as:

$f(x)\to-f(x)$

So, the new function or the reflected function is the negative of the original function.

Therefore, the reflected function $g(x)$ is given as:

$g(x)=-f(x)\\\\g(x)=-4(\frac{1}{2})^x$

Hence, the function that represents the reflection of the given function across the x-axis is $g(x)=-4(\frac{1}{2})^x$