The graph shows the function f(x)=|x|+2 . Place the appropriate symbols in the equation of g(x) so that g(x) is a transformation of f(x) that follows the rule rx−axis .

(1 point)
g(x)=
|x|
2

1 answer

To perform a reflection of the function \( f(x) = |x| + 2 \) across the x-axis, we take the negative of the entire function.

Thus, the transformation for \( g(x) \) is:

\[ g(x) = -(|x| + 2) \]

To break that down, we can rewrite it as:

\[ g(x) = -|x| - 2 \]

So, the equation of \( g(x) \) will be:

\[ g(x) = -|x| - 2 \]

If you need it in the same format as you provided (using placeholders), it could look like:

\[ g(x) = -|x| - 2 \]

where \( \text{insert required symbols} \) would be done in the context of defining the reflection across the x-axis.

If you want to write it in the structure of your initial question:

\[ g(x) = -|x| - 2 \]

This indicates that you are reflecting \( f(x) \) across the x-axis and then translating it down by 2 units.