**Problem : **
If
*f* (*x*)
is stretched vertically by a factor of
and then moved up
6 units and right 4 units, what is the equation of the new function? Give your
answer in terms of
*f* (*x*)
.

**Problem : **
If
*f* (*x*)
is reflected over the
*y*
-axis, then shifted 4 units left and 2 units
down, what is the equation of the new function? Give your answer in terms of
*f* (*x*)
.

**Problem : **
If
*f* (*x*) = 6*x* - 2
, what is the equation of the new function if the graph is
shifted 3 units up and then reflected over the
*x*
-axis?

**Problem : **
If
*f* (*x*) = 3*x*
^{2} - 5
, what is the equation of the new function if the graph if
stretched horizontally by a factor of
, then shifted right 3 units,
then stretched vertically by a factor of
?

**Problem : **
If
*f* (*x*) = *x*
^{3} +6*x*
^{2}
, what is the equation of the new function if the graph is
rotated
180^{
o
}
around the origin, shifted left 7 units, then shifted up 9
units?

**Problem : **
(2, 3) is a point on the graph of
*f* (*x*)
. If the graph is stretched vertically
by a factor of 4, stretched horizontally by a factor of 5, then shifted down 2
units and right 7 units, what is the corresponding point on the new graph?