# How do I find equation for this curve in its final position? The graph of y=sin(x) is shifted a distance of π/4 to the right, reflected in the x-axis, then translate one unit upward

Mar 20, 2018

$y = - \sin \left(x - \frac{\pi}{4}\right) + 1$

#### Explanation:

For a horizontal translation "h" to the right, replace the "x" by $\left(x - h\right)$.
A reflection in the x-axis is a vertical reflection, so all the "y" values are multiplied by $- 1$, so put a negative sign in front of the sin function.
To translate 1 unit up, put $+ 1$ at the end.
Thus, $y = \sin \left(x\right)$ becomes $y = - \sin \left(x - \frac{\pi}{4}\right) + 1$ after the transformations you mentioned,

The order of the transformations is BEDMAS order, namely do the multiplicative transformations first for each direction. The memory aid is RST -- reflections, stretch/compressions, and translations in that order.. The y values are reflected before they are translated 1 up. The x values in this question are only translated, but if there was a horizontal stretch or reflection, that operation would precede the horizontal translation..