Find g(x), where g(x) is the translation 6 units up of f(x)=–2x–5.

To find g(x), which is the translation of f(x) = -2x - 5 up by 6 units, you simply add 6 to the function f(x).

Step 1: Identify the original function, which is f(x) = -2x - 5.

Step 2: Determine the translation direction and magnitude. In this case, it is 6 units up.

Step 3: Apply the translation to the function. Translating a function up or down involves adding or subtracting a constant to the function. Since we are translating up by 6 units, we add 6 to the function.

So, g(x) = f(x) + 6 = -2x - 5 + 6.

Step 4: Simplify the function, if necessary. In this case, -5 + 6 simplifies to 1.

So, g(x) = -2x + 1.

Therefore, the function g(x), which is the translation of f(x) = -2x - 5 up by 6 units, is g(x) = -2x + 1.