Final answer:
The graph of g(x)=-5|x-3|-6 involves a horizontal shift to the right by 3 units, a vertical stretch by a factor of 5 and reflection across the x-axis, and a vertical shift downward by 6 units, which results in a V-shaped graph opening downwards.
Step-by-step explanation:
The transformation that occurs to create the graph of g(x)=-5|x-3|-6 involves several steps. This function is based on the absolute value function y=|x|, which has a V-shape centered at the origin. The transformations applied to this base function include a horizontal shift, a vertical stretch, a reflection in the x-axis, and a vertical shift.
- The term |x-3| represents a horizontal shift to the right by 3 units.
- The multiplier -5 before the absolute value function indicates two transformations: a vertical stretch by a factor of 5 and a reflection across the x-axis because of the negative sign.
- Lastly, the -6 at the end of the function indicates a vertical shift downward by 6 units.
Combining these transformations, the graph of g(x) would be a V-shaped graph that opens downwards, is 5 times steeper than the basic absolute value graph, is shifted 3 units to the right, and is shifted 6 units down.