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.

Answer 1

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