The graph of f(x) = -12|x - 15| - 18 is the graph of the parent absolute value function after it is subjected to a horizontal shift 15 units to the right, then a vertical stretch by a factor of 12, followed by a reflection in the x-axis, and finally a vertical shift 18 units down.
In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:
y = a|x - h| + k.
Where:
- h and k are the vertex of the graph.
- a is a numerical constant.
By critically observing the equation of the transformed absolute value function, we can logically deduce that the parent absolute value function g(x) = |x| was horizontally shifted to the right by 15 units, then a vertically stretched by a factor of 12, followed by a reflection in the x-axis, and finally vertically shifted 18 units down as follows;
g(x) = a|x - h| + k.
f(x) = -12|x - 15| - 18