Final answer:
The given equation f(x) = (7/8) |x + 3| - 9 undergoes three transformations: horizontal translation, vertical compression, and vertical shift. The graph is shifted 3 units to the left, compressed vertically, and shifted 9 units downwards.
Step-by-step explanation:
The given equation is f(x) = (7/8) |x + 3| - 9. Let's analyze the transformations one by one.
Transformation 1:
For the transformation |x + 3|, the graph of the function will be translated horizontally by 3 units to the left.
This means that the vertex of the absolute value graph will be at (-3, 0), instead of (0, 0).
Transformation 2:
The coefficient (7/8) before |x + 3| stretches or compresses the graph of the absolute value function vertically. Since the coefficient is less than 1, the graph will be vertically compressed.
For example, if we had y = |x| and multiplied it by 1/2, the graph would become flatter. Similarly, multiplying by 7/8 will make the graph flatter vertically.
Transformation 3:
The final transformation is subtracting 9 from the entire function. For each point on the graph, the y-coordinate will be shifted 9 units downwards.