**Problem : **
If
*f* (*x*) = (*x* + 2)^{2} - 1
, what is the equation of the function if the graph is
stretched:

a) vertically by a factor of 3

b) vertically by a factor of

c) horizontally by a factor of 2

d) horizontally by a factor of

b)

c)

d)

**Problem : **
What is the equation if
*f* (*x*)
is stretched vertically by a factor of 4 and
shrunk horizontally by a factor of 5 (stretched by a factor of
)?
Give your answer in terms of
*f* (*x*)
.

**Problem : **
What is the equation if
*f* (*x*)
is shrunk vertically by a factor of 6 and shrunk
horizontally by a factor of 6?

**Problem : **
A function passes through (3, 5). It is stretched horizontally by a factor of
2*z* - 1
, and the corresponding part of the resulting function passes through
(9, 5). Solve for
*z*
.

**Problem : **
If
*f* (*x*)
has a domain of and a range of , what are the domain and range of the following:

a)
*g*(*x*) = 10*f* (*x*)

b)
*g*(*x*) = *f* (2*x*)

c)
*g*(*x*) =
*f* (
*x*)

b) Domain: . Range:

c) Domain: . Range:

**Problem : **
What relationship does
*g*(*x*) =
*f* (
*x*)
have to
*f* (*x*)
?