Question

the graph of f (x) and g (z) are shown. The graph of g (x) is the reflection of the graph of f (x) across the x axis. If f (x)=3(1/2)^x what is the equation of g (x)?• g(x) = -3(1/2)^x -6• g(x) = -3(1/2)^x• g(x) = 3(2)^x• g(x) = -3(2)^x• g(x) = 3(1/2)^x. -6

Answer 1

To reflect a function over the x-axis, you have to change the sign of the function, you can express this as:

$g(x)=-f(x)$

We know that the function f(x) has the following formula

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

Then, after the reflection over the x-axis, the function will have the following shape:

$\begin{gathered} g(x)=-f(x) \\ g(x)=-3(\frac{1}{2})^x \end{gathered}$

The correct option is the second one g(x)=-3(1/2)^x