Let gx be the reflection of fx = x² + 3 on the x-axis. What is the function rule for gx?

To find the function rule for gx, we need to understand what it means to reflect a function across the x-axis.

The original function is given as f(x) = x² + 3. When we reflect a function over the x-axis, we negate the output values of the function. This means we will take f(x) and replace it with -f(x).

So, we can express the reflection gx of the original function as:

g(x) = -f(x)

This translates to:

g(x) = -(x² + 3)

Now, simplifying this gives:

g(x) = -x² – 3

Thus, the function rule for gx, the reflection of f(x) across the x-axis, is g(x) = -x² – 3.