Final answer:
To translate a function up 2 units, add 2 to the equation. To reflect a function over the x-axis, negate the entire equation. Start with f(x) = (1/2)|x + 4| - 5. Add 2 to get f(x) = (1/2)|x + 4| - 3. Negate the equation to get f(x) = -(1/2)|x + 4| + 3.
Step-by-step explanation:
To translate a function up 2 units, we add 2 to the function's equation. To reflect a function over the x-axis, we negate the entire function's equation. Therefore, to find the equation that represents f(x) after a translation up 2 units followed by a reflection over the x-axis, we start with the original function f(x) = (1/2)|x + 4| - 5.
First, we translate the function up 2 units by adding 2 to the equation: f(x) = (1/2)|x + 4| - 5 + 2 = (1/2)|x + 4| - 3.
Next, we reflect the function over the x-axis by negating the entire equation: f(x) = -((1/2)|x + 4| - 3) = -(1/2)|x + 4| + 3.