# How do you translate the graph of y=sin(x-pi/4)+1/2?

Mar 1, 2018

The characteristics of the function helps determine how to translate the graph.

#### Explanation:

The general form of a sin function can be written like so:

a sin b(x−c) + d

a: vertical scale; so if $a > 1$, the function will be vertically stretched. Likewise if $a < 1$, the function will be vertically compressed.

b: horizontal scale; so if $b > 1$, the function will be horizontally compressed. Likewise, if $b < 1$, the function will be horizontally stretched.

c: horizontal shift (left/right); so if c is negative, the function will shift to the left. Likewise if c is positive, the function will shift to the right. Beware, since c is in brackets, so let's say (x−6), the 6 is actually considered to be positive, and so the function will shift right, and not left.

d: vertical shift (up/down); so if d is negative, the function will shift down. Likewise, if d is positive, the function will shift up.

The graph of $y = \sin \left(x - \frac{\pi}{4}\right) + \frac{1}{2}$ deals with c and d, so, the function will be translated both horizontally and vertically. C is positive $\frac{\pi}{4}$, so the function will shift $\frac{\pi}{4}$ units right. D is positive $\frac{1}{2}$, so the function will shift $\frac{1}{2}$ units up.