Question

Which function represents g(x), a reflection of f(x) =1/2(3)x across the y-axis?

Answer 1

g(x) = (1/2)3^-x  reflection over y axis yields (-x,y)                                            

Answer 2

Answer:

The required function -  $g(x)=\frac{1}{2}(3)^{-x}$

Step-by-step explanation:

Given : Function represents g(x), a reflection of $f(x) =\frac{1}{2}(3)^x$ across the y-axis

To find : Which function represents the g(x)?

Solution :

The function $f(x) =\frac{1}{2}(3)^x$

The function f(x) reflected across y-axis to form g(x)

The reflection of the point (x,y) across  the y-axis is the point (-x,y).

f(x,y)→f(-x,y) , the graph of f(x) is reflected across y-axis.

Let $y=\frac{1}{2}(3)^x$

After reflection across y-axis is

$g(x)=\frac{1}{2}(3)^{-x}$

The required function.

Refer the attached graph below.