Question

Describe the translations of g(x) that result in h(x).
G(x) = 7x; h(x) = 7/5x - 3.

Answer 1

To obtain h(x) from g(x), the graph is first compressed vertically by a factor of 7/5 and then translated downwards by 3 units.

Step-by-step explanation:

The student is asking about the transformations that occur when the function g(x) = 7x is changed to h(x) = 7/5 - 3). To describe the transformations, we note two changes:

1. Vertical scaling by a factor of 7/5.
2. Vertical translation (downward) by 3 units

First, the coefficient of x is changed from 7 to \(\frac{7}{5}\), which means that the original graph of g(x) is compressed vertically by a factor of \(\frac{7}{5}\). Then, the graph is translated vertically downwards by 3 units due to the subtraction of 3, resulting in the new function h(x).