Question

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

Answer 1

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 (x- pi/4) +1/2` deals with c and d, so, the function will be translated both horizontally and vertically. C is positive `pi/4`, so the function will shift `pi/4` units right. D is positive `1/2`, so the function will shift `1/2` units up.