for b, over the x or y axis?; shift downwards or upwards? for c, shift to the ri

Question

for b, over the x or y axis?; shift downwards or upwards?

for c, shift to the right or left?; across the x or y axis?

for d, across the x or y axis?

Match each of the following functions with its graph, and identify the transformations that took place on the parent (original) function a. f(x) -(x 2)3 3; Shift of the graph of xto the b. g(x) - -x3-2; The graph of x reflected over the c. h(x) =-61n(x + 1); by followed by a shift by followed by a shift of Shift to the by of In(x)'s graph followed by a reflection across the and a stretch by a factor of d. k(x) =-6e-X; Graph of eX first reflected across the then reflected across the x-axis and finally is stretched by a factor of 12x -6 -4.2 Graph A Graph B Graph C Gaph D

Explanation / Answer

a)To shift a function left, add inside the function's argument: f(x + b) givesf(x) shifted b units to the left. Shifting to the right works the same way; f(x – b) is f(x)shifted b units to the right.

f(x) = x^3 shifted right by 2 units to get (x-2)^3 followed by vertical shift of 3 units upwards.

b) The grapoh of x^3 reflected over the x axis to get -x^3 further a vertical shift down of 2 units

c) h(x) = -6ln(x+1)

Shift to left by 1 units reflect over the x axis stettch by 6 units

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