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

Question

Zoe Austin · Accepted Answer

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

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.