Questions: The graph of f(x) is shown below as a red dashed curve. Drag the movable blue points to obtain the graph of g(x) = 3/2 f(x-3), shown as a blue solid curve. The coordinates of the vertex and an additional point are shown for both curves.

Solution Steps

The given function transformation is \( g(x) = \frac{3}{2} f(x-3) \). This involves two transformations:

1. Horizontal shift to the right by 3 units.
2. Vertical stretch by a factor of \(\frac{3}{2}\).

Shift the graph of \( f(x) \) to the right by 3 units. This means every point \((x, y)\) on the graph of \( f(x) \) will move to \((x+3, y)\).

After shifting, apply the vertical stretch by multiplying the y-coordinates by \(\frac{3}{2}\). This means every point \((x+3, y)\) will become \((x+3, \frac{3}{2}y)\).

Final Answer