Find g(x), where g(x) is the reflection across the x-axis of f(x)=–8|x–2|+3.g(x)=8|x–2|+3g(x)=8|x–2|–3g(x)=–8|x–2|–3g(x)=–8|x–2|+3Submit

The reflection of a function across the x-axis simply changes the sign of the output of the function. So, if f(x) = -8|x-2|+3, then the reflection of f(x) across the x-axis, which we'll call g(x), is g(x) = 8|x-2|+3. This is because the absolute value function |x-2| is always positive, and the negative sign in front of the 8 in f(x) makes the output of the function negative. When we reflect across the x-axis, we change the sign of the output, so the negative becomes positive. The +3 at the end of the function remains the same, because it is a vertical shift and does not affect the reflection.