Final answer:
To vertically shrink the function f(x) = -4|x - 2| by a factor of 1/2, multiply the entire function by 1/2. The resulting function is g(x) = -2|x - 2|.
Step-by-step explanation:
To apply a vertical shrink by a factor of 1/2 to the function f(x) = -4|x - 2|, you would multiply the output of the function, which is -4|x - 2|, by 1/2. This transformation results in a new function:
g(x) = (1/2) × f(x) = (1/2) × (-4|x - 2|) = -2|x - 2|.
The new function g(x) represents the original function after the vertical shrink has been applied. The absolute value ensures the function remains non-negative and the negative sign in front of the constant multiplies these non-negative values by negative two, reflecting them across the x-axis.