Can the function g be obtained from f by transformations? If so, describe the transformations needed? The function f and g are described algebrically as follows: f(x)=(x+2)2 g(x)=(x−2)2+5

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Can the function g be obtained from f by transformations? If so, describe the transformations needed?  The function f and g are described algebrically as follows:  f(x)=(x+2)2  g(x)=(x−2)2+5

Liek1993 · Accepted Answer

Step 1  Given functions  f(x)=(x+2)2  g(x)=(x−2)2+5  Yes, the function g(x) can be obtained by f(x) by transformation.  Step 2  Point (1)  If we are shifting the curve of f(x) by 4 units right on x−axis, then we have to subtract 4 from x in f(x) to get new function.  In that case, f(x) will become   (x−4+2)2=(x−2)2  Point (2)  If we are shifting the curve of f(x) by 5 units on positive y−axis then there will be addition of 5 in f(x).  In that case, f(x) will become  (x+2)2+5  If both the points are applicable at one time, then wecan get g(x)  g(x)=(x−4+2)2+5  g(x)=(x−2)2+5   So, the given statement is true.

Can the function g be obtained from f by transformations? If so, describe the tr

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