If ƒ(x) = x + a, where a is a positive integer, write the equation of the new function if ƒ(x) is translated (1) UP a units.

Question

If ƒ(x) = x + a, where a is a positive integer, write the equation of the new function if ƒ(x) is translated

(1) UP a units.
(2) DOWN a units.
(3) UP 4 units.
(4) DOWN 1 units.

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    2021-11-26T07:34:28+00:00

    The graphs of the functions can be transformed, obtaining related functions.We consider two kinds of transformations.
     Vertical and horizontal displacements: It is assumed that c is a positive
     constant, ie c> 0 and y = f (x) then
     y = f (x) + c moves the graph c units up.
     y = f (x) – c moves the graph c units down.
     y = f (x + c) shifts the graph c units to the right.
     y = f (x – c) shifts the graph c units to the left

     (1) UP a units.
     ƒ (x) = x + a
     new function
     g (x) = x + a + a
     g (x) = x + 2a

     (2) DOWN a units.
     ƒ (x) = x + a
     new function
     g (x) = x + a – a
     g (x) = x

     (3) UP 4 units.
     ƒ (x) = x + a
     new function
     g (x) = x + a + 4

     (4) DOWN 1 units
     ƒ (x) = x + a
     new function
     g (x) = x + a – 1

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