Find which transformation had to be done to graph the red curve g\left(x\right) from the blue one f\left(x\right).
The blue graph opens up and any shift or horizontal reflection keeps the direction. So the only possibility is that the red curve is a vertical reflection of the blue curve.
The red curve is an vertical reflection of the blue curve.
We can see that the line x=0 is the axis of symmetry. Therefore
The red curve is an horizontal reflection of the blue curve.
Since the direction of the graphs are the same, we conclude that it is a downward shift of 4 units.
It is a downward shift of four units.
Since any shift or horizontal reflection keeps the direction. So the red curve is a vertical reflection of the blue curve. The axis of symmetry is the line y=0
The red curve is an vertical reflection of the blue curve.
Since the direction is not changed so it can not be a vertical reflection. It could be a horizontal reflection but the axis of symmetry is not the y -axis. So the only possibility is a shift. We can see that the red curve is 3 units on the right of the blue one, so it is a shift to the right.
a shift of 3 units to the right
We can see that the line y=x is the axis of symmetry. So it is a reflection across the line y=x
It is a reflection across the line y=x.
We can see that the line y=1 is the axis of symmetry. So it is a horixontal reflection across the line y=1
The red curve is an horizontal reflection of the blue curve.