2. A translation is an operation that
shifts a graph horizontally, vertically, or
both. The result is a graph that is the
same shape and size, located in a
different position. The variables h and k
are commonly used to represent the
general form of a translation. Vertical
translations are represented by the value
for k, while h is the variable used to
represent horizontal translations.
4. The graph of a function of the form
y = k + sin x and y = k + cos x is translated
vertically as compared with the graph of
y = sin x and y = cos x .
The Translation is k units up if k > 0
and l k l units down if k < 0 .
Note : k represents the vertical translation of the sine and cosine
function
5. Note : By changing the constant
that is added or subtracted to the
basic sin or cosine curve, we affect
how the graph is shifted up or down.
This is called vertical translation or
vertical shift.
6. The Vertical Translation of y = 2 + sin x and y = -1+ sin x
y = 2 + sin x is translated 2 units upward because k is 2 and y = -1+ sin x is translated
downward because the value of k is -1 .
