Naeethaasavage
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The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).

The function f is defined as follows fx 4x6 If the graph of f is translated vertically upward by 4 units It becomes the graph of a function g Find the expressio class=

Respuesta :

Answer:

g ( x ) = 4x^2 + 10

Step-by-step explanation:

Solution:-

The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines

    Horizontal shifts

  • Right :  f ( x ) -> f ( x - a )
  • Left :  f ( x ) - > f ( x + a )

   

  Vertical shifts

  • Up :  f ( x ) -> f ( x ) + b
  • Down :  f ( x ) - > f ( x ) - b

   General shift ( Horizontal and Vertical shift )

               f ( x ) - > f ( x ± a ) ± b

We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

                        f ( x ) = 4x^2 + 6

                        f ( x ) - > f ( x ) + b              

                        g ( x ) = f ( x ) + 4

                        g ( x ) = 4x^2 + 6 + 4

                        g ( x ) = 4x^2 + 10   ... Answer

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