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Operations on Functions

Problems

Stretches and Shrinks

Reflections and Rotations

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

a) g(x) = 3(x + 2)2 - 4
b) g(x) = (x + 2)2 -
c) g(x) = ( x + 2)2 = (x + 4)2 - 1
d) g(x) = (4x + 2)2 -1 = 16(x + )2 - 1

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) .

4f (5x)

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

f (6x)

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

z = 2

Problem : If f (x) has a domain of and a range of , what are the domain and range of the following:
a) g(x) = 10f (x)
b) g(x) = f (2x)
c) g(x) = f ( x)

a) Domain: . Range:
b) Domain: . Range:
c) Domain: . Range:

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

g(x) is shrunk vertically by a factor of 2 (stretched by ) and stretched horizontally by a factor of 3.

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