Question

Which function represents g(x), a reflection of f(x) = 6(1/3)^x across the y-axis?

Answer 1

Answer:

$g(X) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^{-x}$            

Step-by-step explanation:

We are given the function:

$f(x) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^x$

We have to find another function g(x) that is reflection of f(x) across, the y-axis.

To find the reflection of the function, we put -x in place of x to find the reflection of given function.

Thus, reflection of f(x) is given by g(x), where,

$g(x)=f(-x) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^{-x}$

The attached image shows the function and the reflection of function across y-axis.

Answer 2

Answer:

g(x)= $6(\frac{1}{3})^{-x}$

Step-by-step explanation:

a reflection of f(x) = 6(1/3)^x across the y-axis

Given f(x)= $6(\frac{1}{3})^x$

When graph of f(x) reflects across y axis then f(x) becomes f(-x)

For reflection across y axis we replace x  with -x

f(x)= $6(\frac{1}{3})^x$

f(-x)= $6(\frac{1}{3})^{-x}$

f(-x) is a reflection across the y axis  that is our g(x)

So g(x)= $6(\frac{1}{3})^{-x}$