Describe how the graph of y=f(-2x+6)+7 can be obtained from the graph y=f(x)
To obtain the graph of y = f(-2x + 6) + 7 from the graph of y = f(x), you need to perform a series of transformations. Here is a step-by-step explanation on how to achieve this:
1. Horizontal Reflection: Reflect the original graph of y = f(x) across the y-axis. This can be achieved by replacing x with -x. The equation becomes y = f(-x).
2. Horizontal Compression: Compress the horizontally reflected graph by a factor of 2. This can be done by replacing x with -2x. The equation becomes y = f(-2x).
3. Horizontal Translation: Translate the horizontally compressed graph 6 units to the right. This can be achieved by subtracting 6 from the argument -2x. The equation becomes y = f(-2x + 6).
4. Vertical Translation: Finally, shift the translated graph 7 units upward. This can be done by adding 7 to the equation. The final equation becomes y = f(-2x + 6) + 7.
By following these steps, you can obtain the graph of y = f(-2x + 6) + 7 from the graph of y = f(x).