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Question 850606: To graph the function g(x) = (1/12)(sqrtx-3) + 10, start with the graph of f(x) = (sqrtx) and then make which of the following changes?
A. Shift the graph of f left by 10 units.
B. Shift the graph of f right by 10 units.
C. Shift the graph of f up by 10 units.
D. Shift the graph of f down by 10 units.
E. Shift the graph of f left by (1/12), unit.
F. Shift the graph of f right by (1/12), unit.
G. Shift the graph of f up by (1/12), unit.
H. Shift the graph of f down by (1/12), unit.
I. Shift the graph of f left by 3 units.
J. Shift the graph of f right by 3 units.
K. Shift the graph of f up by 3 units.
L. Shift the graph of f down by 3 units.
M. Reflect the graph of f over the x-axis.
N. Reflect the graph of f over the y-axis.
O. Stretch the graph of f vertically.
P. Shrink the graph of f vertically.
Q. Stretch the graph of f horizontally.
R. Shrink the graph of f horizontally.
[ Note: Do not simplify g(x) or rewrite it in another form before determining the appropriate transformations.]
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! To graph the function g(x) = (1/12)(sqrtx-3) + 10, start with the graph of f(x) = (sqrtx) and then make which of the following changes?
A. Shift the graph of f left by 10 units.
B. Shift the graph of f right by 10 units.
C. Shift the graph of f up by 10 units. (because of the +10 tacked on at the end)
D. Shift the graph of f down by 10 units.
E. Shift the graph of f left by (1/12), unit.
F. Shift the graph of f right by (1/12), unit.
G. Shift the graph of f up by (1/12), unit.
H. Shift the graph of f down by (1/12), unit.
I. Shift the graph of f left by 3 units.
J. Shift the graph of f right by 3 units. (because of the x-3 in the radicand)
K. Shift the graph of f up by 3 units.
L. Shift the graph of f down by 3 units.
M. Reflect the graph of f over the x-axis.
N. Reflect the graph of f over the y-axis.
O. Stretch the graph of f vertically.
P. Shrink the graph of f vertically. (because of the 1/12)
Q. Stretch the graph of f horizontally.
R. Shrink the graph of f horizontally.
Side Note:
The order in which the transformations are applied is: P, J, C
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