If this is the one you are talking about then:
horizontal translation of 3 units is: y= f(x-3)
vertical stretch by a scale factor of 3 is: y= 3f(x)
reflection over the x-axis is: y= -f(x)
vertical translation of 3 units is: y= f(x)+3
Step-by-step explanation:
Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.
Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).
Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).
Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).
