The function is
.
Basic function is
.
, shift the graph of
units up.
Replace
by
.
Obtain the graph of
from basic function
, add
to each
-coordinate on graph of basic function.
Choose random values for
and find the corresponding values for
.
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Graph:
\Draw a coordinate plane.
\Plot the points of the basic function
and connect these points with smooth curve.
Plot the points of the
are
and connect these points with smooth curve.
.
Observe the graph:
\The graph of
is identical to
except that it is vertically shifted up
units.
The domain of the
is all real numbers.
Domain of
in the interval notation:
.
Range of
is 
Range of
in the interval notation:
.
Graph:
\Domain of
in the interval notation:
.
Range of
in the interval notation:
.