QuestionConvert the following function notation into words and then point notation. $$g(x) \rightarrow 2 g(3 x)+2$$

Studdy Solution
To convert the transformation into point notation, we need to apply the transformations to a generic point $(x, y)$ on the graph of $g(x)$:
1. Horizontal compression by a factor of $\frac{1}{3}$ changes the x-coordinate: $(x, y) \rightarrow \left(\frac{x}{3}, y\right)$
2. Vertical stretch by a factor of 2 changes the y-coordinate: $\left(\frac{x}{3}, y\right) \rightarrow \left(\frac{x}{3}, 2y\right)$
3. Vertical shift upwards by 2 units changes the y-coordinate: $\left(\frac{x}{3}, 2y\right) \rightarrow \left(\frac{x}{3}, 2y + 2\right)$
Thus, the point notation for the transformation is: $(x, y) \rightarrow \left(\frac{x}{3}, 2y + 2\right)$
The transformation in point notation is $(x, y) \rightarrow \left(\frac{x}{3}, 2y + 2\right)$.