What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?
2 answers:
Answer:
vertical translation of 3 units down
Step-by-step explanation:
we have
The vertex of the graph of f(x) is the point (0,0)
The vertex of the graph of g(x) is the point (0,-3)
see the attached figure to better understand the problem
so
The transformation of f(x) to g(x) is
f(x) -----> g(x)
(0,0) -----> (0,-3)
(x,y) -----> (x,y-3)
That means -----> The translation is 3 units down
therefore
vertical translation of 3 units down
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The option are missing in the question. The options are :
A. P = 2, a = 1
B.
C.
D. P = 2, a = 3
Solution :
The given function is
So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.
When the four option being substituted in the function, we get
A). It is a constant function since
B). Here, the value of a is a fraction which is less than 1, so it is a decay function.
C). It is a constant function since the value of a is 1.
D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.
Therefore, option (D). represents an exponential function.