Question 1153574: The graph of
f(x) = -1/2 (1/6)exponent is x-7
+9 is shifted left 7 units, stretched vertically by a factor of 6, reflected about the x-axis, and then shifted downward 9 units. What is the equation of the new function, g(x)?
g(x) =
State the y-intercept of
g(x).
(x, y) =
State the domain and range of
g(x).
(Enter your answers using interval notation.)
domain
range
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! SHIFTS OF THE PARENT FUNCTION:
For any constants  ,  and  , the function
-is stretched vertically by a factor of if 
-is compressed vertically by a factor of if 
-has a y-intercept of ( ,)
-shifts the parent function vertically units, in the same direction of the sign of 
-horizontally units, in the opposite direction of the sign of
-the y-intercept becomes (, )
-the horizontal asymptote becomes 
-the range becomes (, ).
-the domain, ( ,), remains unchanged
in your case we have 
the equation of the new function,  :
- is shifted left  , so we have
-stretched vertically by a factor of , so we have
-reflected about the  -axis, so we have
and then shifted downward  units, so we have
State the y-intercept of .
(,  ) =(, )
the domain and range of :
the range becomes (,)
the domain, ( ,)
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