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Operations on Functions

Problems

Reflections and Rotations

Combining Operations on Graphs

Here is the graph of y = f (x) :


Graph of y = f (x)

Problem : Graph y = - f (x) .


Graph of y = - f (x)

Problem : Graph y = f (- x) .


Graph of y = f (- x)

Problem : Graph x = f (y) .


Graph of x = f (y)

Problem : Graph y = - f (- x) .


Graph of y = - f (- x)

Problem : If f (x) = 4x - 6 , what is the equation of the function if:
a) The graph is reflected over the x -axis.
b) The graph is reflected over the y -axis.
c) The graph is rotated 180 o around the origin.

a) g(x) = - 4x + 6 .
b) g(x) = - 4x - 6 .
c) g(x) = 4x + 6 .

Problem : If f (x) = 16x 2 - 3x + 4 , what is the equation of the function if:
a) The graph is reflected over the y -axis.
b) The graph is reflected over the x -axis.
c) The graph is rotated 180 o around the origin.

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

Problem : If f (x) = x 3 , what is the equation of the function if:
a) The graph is reflected over the x -axis.
b) The graph is reflected over the y -axis.
c) The graph is rotated 180 o around the origin.

a) g(x) = - x 3 .
b) g(x) = - x 3 .
c) g(x) = x 3 .

Problem : The domain of a function is and the range of a function is , what are the domain and range if:
a) The graph is reflected over the x -axis.
b) The graph is reflected over the y -axis.
c) The graph is rotated 180 o around the origin.

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

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