Question

List the transformations needed to transform the graph of h(x) = 5ˣ into the graph of the given equation. (Enter each answer as a whole number.) g(x) = -4 (5ˣ⁵)+3

Answer 1

The graph of h(x) = 5ˣ can be transformed into the graph of g(x) = -4(5ˣ⁵)+3 by applying a vertical compression by a factor of 4 and a vertical shift upward by 3 units.

Step-by-step explanation:

To transform the graph of h(x) = 5ˣ into the graph of g(x) = -4(5ˣ⁵)+3, we need to apply the following transformations:

1. Vertical stretch/compression: The coefficient in front of 5ˣ indicates the vertical stretch/compression. In this case, the coefficient is -4, which means the graph is compressed vertically by a factor of 4.
2. Vertical shift: The constant term in the equation (+3) indicates a vertical shift. In this case, the graph is shifted upward by 3 units.

Therefore, the transformations needed are a vertical compression by a factor of 4 and a vertical shift upward by 3 units.

Learn more about Transformations of Exponential Functions