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Operations on Functions

Problems

Combining Operations on Graphs

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Problem : If f (x) is stretched vertically by a factor of and then moved up 6 units and right 4 units, what is the equation of the new function? Give your answer in terms of f (x) .

f (x - 4) + 6 .

Problem : If f (x) is reflected over the y -axis, then shifted 4 units left and 2 units down, what is the equation of the new function? Give your answer in terms of f (x) .

f (- x - 4) - 2 .

Problem : If f (x) = 6x - 2 , what is the equation of the new function if the graph is shifted 3 units up and then reflected over the x -axis?

g(x) = - (f (x) + 3) = - 6x - 1 .

Problem : If f (x) = 3x 2 - 5 , what is the equation of the new function if the graph if stretched horizontally by a factor of , then shifted right 3 units, then stretched vertically by a factor of ?

g(x) = f (2x - 6) = (2x - 6)2 - .

Problem : If f (x) = x 3 +6x 2 , what is the equation of the new function if the graph is rotated 180 o around the origin, shifted left 7 units, then shifted up 9 units?

g(x) = - f (- x - 7) + 9 = x 3 -6x 2 + 16 .

Problem : (2, 3) is a point on the graph of f (x) . If the graph is stretched vertically by a factor of 4, stretched horizontally by a factor of 5, then shifted down 2 units and right 7 units, what is the corresponding point on the new graph?

(17, 10)

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