Final answer:
The function g(x) that represents a horizontal stretch by a factor of 4 of the function f(x) = |x + 3| is g(x) = |(x/4) + 3|.
Step-by-step explanation:
To create a function g that represents a horizontal stretch by a factor of 4 of the function f(x) = |x + 3|, you need to adjust the input to the original function. When we stretch a graph horizontally by a factor of a, we replace every x in the function with x/a.
Therefore, to stretch the graph of f(x) horizontally by a factor of 4, the new function g(x) will have the form
g(x) = |(x/4) + 3|.
A simple example to visualize this would be to observe how the point that was originally at x = -3 (which makes f(x) = 0) would still make g(x) = 0, while a point that was at x = 1 that originally made f(x) = 4, would now be at the point x = 4 on g(x), since 1/4 is stretched to 1 through multiplication by 4, and 1 + 3 equals 4.
Thus, we've confirmed the horizontal stretch.