Write the equation for the transformation of the graph of y = f (x). Show your work.
translated 2 units left, 7 units down
The transformation of the graph of y = f(x) that is translated 2 units left and 7 units down can be denoted as y = f(x + 2) - 7.
Explanation:
To translate the graph 2 units to the left, we subtract 2 from the x-coordinate. This can be done by replacing x with (x + 2) since any value of x will be 2 units less than the original value.
To translate the graph 7 units down, we subtract 7 from the y-coordinate. This can be done by subtracting 7 from f(x). Therefore, the equation becomes y = f(x + 2) - 7.