Operations on Functions

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

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) .

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?

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

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

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