Given the graph of f(x) find the graph of 2 f( -3x - 2) - 4
Is this correct???
First, compress the graph horizontally by 3. Second, reflect the graph over the y-axis. Third, shift the graph 2 units to the right. Fourth, stretch the graph vertically by 2. Lastly, shift the graph 4 units downward.
Yes, your steps are correct! Here's a breakdown of each step in finding the graph of 2f(-3x - 2) - 4 based on the original graph of f(x):
1. Compress the graph horizontally by 3:
To compress the graph horizontally by 3, you need to divide the x-values by 3. This means that each x-coordinate on the original graph will become x/3 on the new graph.
2. Reflect the graph over the y-axis:
To reflect the graph over the y-axis, you simply change the sign of each x-coordinate on the graph. So, if the original graph had points (a, b), they will become (-a, b) on the new graph.
3. Shift the graph 2 units to the right:
To shift the graph 2 units to the right, you need to add 2 to each x-coordinate. The new coordinates will become (x + 2, y).
4. Stretch the graph vertically by 2:
To stretch the graph vertically by a factor of 2, you multiply the y-coordinates by 2. This means that each point (x, b) on the graph will become (x, 2b) on the new graph.
5. Shift the graph 4 units downward:
To shift the graph downward by 4 units, you subtract 4 from each y-coordinate. The new coordinates will become (x, y - 4)
By following these steps, you should be able to obtain the graph of 2f(-3x - 2) - 4 based on the given graph of f(x).