Operations on Functions

Math
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Summary

Problems 3

Summary Problems 3

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 180o around the origin.

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

Problem : If f (x) = 16x2 - 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 180o around the origin.

a) g(x) = 16x2 + 3x + 4.
b) g(x) = - 16x2 + 3x - 4.
c) g(x) = - 16x2 - 3x - 4.

Problem : If f (x) = x3, 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 180o around the origin.

a) g(x) = - x3.
b) g(x) = - x3.
c) g(x) = x3.

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 180o around the origin.

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