Final answer:
The transformed function after being vertically stretched by a factor of 4, horizontally stretched by a factor of 3/2, and translated right by 6 units is represented by the equation 4f((2x/3)-4).
Step-by-step explanation:
A student asked about the transformations of a function involving a vertical stretch, a horizontal stretch, and a translation to the right. To represent these transformations on a function f(x), we can apply the following changes to its equation:
- For the vertical stretch by a factor of 4, we multiply the function by 4. If the original function is f(x), the vertically stretched function is 4f(x).
- To achieve a horizontal stretch by a factor of 3/2, we divide the input variable by 3/2, which is the same as multiplying by 2/3. Therefore, the horizontally stretched function becomes f(2x/3).
- Translating the function to the right by 6 units means we substitute (x-6) for x. So the function after the translation is f(2(x-6)/3) or f((2x/3)-4).
Combining all these transformations, the final transformed function is 4f((2x/3)-4).