Margaret accurately grasps the transformations but mislabels a horizontal translation and has a slight terminology error in describing a vertical stretch.
In the given context, two parent functions, f(x) = 2x - 7, undergo different transformations to yield new functions (g(x). Let's evaluate Margaret's identifications and correct any mistakes.
1. For the transformation g(x) = f(x-2), the correct interpretation is a horizontal translation of 2 units to the right. However, Margaret incorrectly identifies this as a vertical translation. The correction is that it's a horizontal translation, not a vertical one.
2. For the transformation g(x) = -2f(x), the correct transformation is a vertical stretch by a factor of 2. Margaret identifies it as a vertical stretch, which is correct in essence. However, her terminology is a bit imprecise as she labels it a "vertical strecth" (presumably a typo). The correct term is a "vertical stretch." Therefore, Margaret's interpretation is conceptually accurate, but the terminology needs correction.
In summary, Margaret correctly identifies the nature of the transformations but makes a terminology error in the first case by labeling a horizontal translation as a vertical one. In the second case, the concept is right, but the term "vertical strecth" needs correction to "vertical stretch."