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Operations on Functions

Problems

Translations

Stretches and Shrinks

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 .

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