Final answer:
The new equation after making a vertical stretch by three, shifting left four units, and shifting up five units is 3| x + 4| + 5.
Step-by-step explanation:
To find the new equation after making a vertical stretch by three, shifting left for units, and up five units, we need to start with the equation for the absolute value parent function. The equation for the parent function is |x|. First, we need to vertically stretch the parent function by three. The new equation becomes 3|x|. Then, we shift the graph left for units, which can be represented by subtracting units from the x inside the absolute value function. The new equation becomes 3| x + 4|. Finally, we shift the graph up five units, which can be represented by adding 5 outside the absolute value function. The new equation becomes 3| x + 4| + 5. Therefore, the new equation after the vertical stretch, shifting left four units, and shifting up five units is 3| x + 4| + 5.