Question

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

Answer 1

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.