The graph shows the function f (x) = lxl + 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.

Question

g (x) = __ lxl ___ 2

Answer 1

To apply a reflection across the x-axis to the function \( f(x) = |x| + 2 \), you need to change the sign of the entire function.

The transformation rule for reflecting across the x-axis is to take the negative of the function. Therefore, the transformation of \( f(x) \) will be:

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

So, filling in the blanks in your equation, we have:

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