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State the various transformations applied to the base function

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State the various transformations applied to the base function ƒ(x) = x2 to obtain a graph of the function g(x) = − (2x)2 − 1.

asked Jun 10, 2014 in PRECALCULUS by bilqis Pupil

1 Answer

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The function is g ( x ) = - (2x)2 - 1.

Rewrite the function as g ( x ) = - 4x2 - 1.

The heighest power of x in g ( x ) = - 4x2 - 1 is 2, so the parent function is square function.

The equation of parent function is f ( x ) = x2 .

The transformation function is g ( x ) = - 4 x2 - 1 and the parent function is f ( x ) = x2 .

So, the functions f and g have the following relationship.

g ( x ) = - 4f ( x ) - 1.

To transform the graph of f ( x ) = x2 into the graph of  g(x) follow the steps :

Step 1 :

The graph of g (x) is the reflection of the graph of f ( x ) in the x - axis.

Then,  the function is g (x) = - x2 .

Step 2 :

The graph of g (x) is the vertical stretch (each y - value is multiplied by 4) of the graph of f (x).

Then,  the function is g (x) = - 4x2 .

Step 3 :

The graph of g (x) is the vertical shift(down ward) of one unit of the graph of f ( x ).

Then, the function is g (x) = - 4x2 - 1.

The functions f and g are related as follows :

answered Jun 10, 2014 by lilly Expert

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