**Problem : **
If *f* (*x*) = (*x* - 3)^{2} - 2, what is the equation of the function if the graph is
shifted:

a) 2 units left

b) 3 units up

c) 8 units right

d) 1 unit down

a)

*g*(*x*) = (*x* - 1)^{2} - 2
b)

*g*(*x*) = (*x* - 3)^{2} + 1
c)

*g*(*x*) = (*x* - 11)^{2} - 2
d)

*g*(*x*) = (*x* - 3)^{2} - 3
**Problem : **
What is the equation if *f* (*x*) is shifted 3 units up and 5 units to the right?
Give your answer in terms of *f* (*x*).

*g*(*x*) = *f* (*x* - 5) + 3
**Problem : **
The domain of a function is and the range of the function is
. What are the domain and range if the function is shifted
left 2 units and up 6 units?

Domain:

Range:

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

a) *g*(*x*) = *f* (*x*) + 4

b) *g*(*x*) = *f* (*x* + 3)

c) *g*(*x*) = *f* (*x* + 3) + 4

a) Domain: . Range:

b) Domain: . Range:

c) Domain: . Range:

**Problem : **
What relationship does *g*(*x*) = *f* (*x* + 2) - 8 have to *f* (*x*)?

*g*(*x*) is shifted 2 units to the left and 8 units down from

*f* (*x*).

**Problem : **
What relationship does *g*(*x*) = *f* (*x* - 1) + 6 have to *f* (*x* + 2) + 5?

*g*(*x*) is shifted 3 units to the right and 1 unit up from

*f* (*x* + 2) + 5.