The graph of a function passes through the points (9,-6) and (12, -3). What are the coordinates of these points after the function has been compressed by a factor of 1/3?
To compress a graph by a factor of 1/3, each x-coordinate is multiplied by 1/3, and each y-coordinate is multiplied by 1/3.
The original coordinates are (9, -6) and (12, -3).
To compress the x-coordinate of (9, -6), we multiply 9 by 1/3:
x' = 9 * 1/3 = 3
To compress the y-coordinate of (9, -6), we multiply -6 by 1/3:
y' = -6 * 1/3 = -2
Therefore, the new coordinates for the point (9, -6) after compressing by a factor of 1/3 are (3, -2).
Similarly, for the point (12, -3):
x' = 12 * 1/3 = 4
y' = -3 * 1/3 = -1
So, the new coordinates for the point (12, -3) after compressing by a factor of 1/3 are (4, -1).
To compress the graph of a function by a factor of 1/3, we need to multiply the x-coordinates of each point by 3 and multiply the y-coordinates of each point by 1/3.
For the point (9, -6), when we compress it, the new x-coordinate will be 9 * 3 = 27, and the new y-coordinate will be -6 * (1/3) = -2.
Therefore, the new coordinates of the point (9, -6) after the function has been compressed by a factor of 1/3 are (27, -2).
Similarly, for the point (12, -3), when we compress it, the new x-coordinate will be 12 * 3 = 36, and the new y-coordinate will be -3 * (1/3) = -1.
Therefore, the new coordinates of the point (12, -3) after the function has been compressed by a factor of 1/3 are (36, -1).