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 r_x-axis

Answer 1

To transform the function \( f(x) = |x| + 2 \) according to the rule \( r_{x\text{-axis}} \), you need to reflect the function across the x-axis.

The transformation that reflects a function \( f(x) \) across the x-axis is given by \( g(x) = -f(x) \). So, for the function \( f(x) = |x| + 2 \), the transformation \( g(x) \) will be:

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

Thus, if you're writing out \( g(x) \) in terms of its transformation from \( f(x) \), you would represent it as:

\[ g(x) = -f(x) \]

This means \( g(x) = -(|x| + 2) \), which yields:

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

So, the appropriate symbols in the equation of \( g(x) \) to indicate the transformation \( r_{x\text{-axis}} \) are a negative sign in front of \( f(x) \).

If this is what you were looking for, the final answer is \( g(x) = -(|x| + 2) \).