Shifting of Function

==2024-11-14

Shifting of $y = f (x)$

Theory

Important

$y = f (x) + a$ → $if a > 0$ shifts up by a units, else down by |a| units. $y = f (x - a)$ → $if a > 0$ shifts right by a units, else left by |a| units.

Examples

For $y = f (x) = x^{2}$ , shiftings:

$y = f (x) + a, a > 0$
$y = x^{2} + 2$ → a>0 : green $y = x^{2} - 2$ →a<0 : purple $y = (x - 2)^{2}$ →a>0 : black $y = (x + 2)^{2}$ →a<0 : red
y=x^2
y=x^2+2
y=x^2-2
y=(x-2)^2
y=(x+2)^2

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