What would be the transformations in this equation?
y = (-x -88) + 76
Also what about this question?
y = .2 sin ( -8x + 50) + 37
Would this be a vertical compression 0.2, horizontal compression -8, horizontal shift 50, and vertical up 37?
Would the one above this one be a reflect over y-axis, right 88 up 76?
(-x-88) = -(x+88)
so, shift left 88, then reflect over y-axis
-8x+50 = -8(x-25/4)
so, shift right by 25/4, then horizontal compression by a factor of 8, and reflect across y-axis.
In the equation y = (-x -88) + 76, there are two main transformations happening: a reflection and a translation.
1. Reflection:
The negative sign in front of the x variable (-x) indicates a reflection in the x-axis. It means that all points on the graph will be mirrored or flipped across the x-axis. For example, if the original point was (x, y), after the reflection it would become (x, -y). This reflection causes the "upside-down" appearance of the graph.
2. Translation:
The numbers -88 and 76 represent a translation of the graph. Specifically, (-x - 88) shifts the graph horizontally to the right by 88 units, and (+76) shifts the graph vertically upwards by 76 units. When performing a horizontal translation, we subtract the translation value from x, while for a vertical translation we add the translation value to y.
These transformations alter the shape, position, and orientation of the graph of the equation y = -x - 88 + 76 compared to the original equation y = -x.