The function is .
The function is a square root function.
\The standard form of the square root function is .
Graph :
\Graph of the root function :
\
The function is .
Now substitute instead of
in the standard square root function.
.
So .
Horizontal shift : , shift the graph of
a distance
units to the left.
Vertical stretch : , stretch the graph of
vertically by a factor of
.
Reflection : , reflect the graph of
about the
axis.
Vertical shift : , shift the graph of
a distance
units upward.
Therefore, is the graph of
shift
units to the left and next stretch vertically by a factor of
.
Now reflect about the axis and shift
unit upward.
Graph :
\Graph of the function .
(1) Draw the coordinate plane.
\(2) Graph of the function .
(3) First shift the graph of to a distance of
units to the left
(4) After that stretch the graph of vertically by a factor of
.
(4) Next reflect the graph of about the
axis.
(5) Now shift the graph of to a distance of
unit upward.
Graph of the function is