Find g(x), where g(x) is the reflection across the y-axis of f(x)=–4|x+5|–10.

To find the reflection of the function f(x) = -4|x+5| - 10 across the y-axis, we replace every x in the function with -x.

Step 1: Identify the original function The original function is f(x) = -4|x+5| - 10.

Step 2: Replace x with -x The new function g(x) will be -4|-x+5| - 10.

Step 3: Simplify the function The absolute value function |a| is always positive, so |-x+5| is the same as |x-5|. Therefore, the reflected function g(x) is -4|x-5| - 10.

So, g(x) = -4|x-5| - 10 is the reflection of the function f(x) = -4|x+5| - 10 across the y-axis.