**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*).

*f* (*x* - 4) + 6.

**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*).

*f* (- *x* - 4) - 2.

**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?

*g*(*x*) = - (*f* (*x*) + 3) = - 6*x* - 1.

**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?

*g*(*x*) = - *f* (- *x* - 7) + 9 = *x*^{3} -6*x*^{2} + 16.

**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?

(17, 10)