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Question Number 148804 by saly last updated on 31/Jul/21

Commented by saly last updated on 31/Jul/21

$C o n s t r u c t a g r a p h o f a f u n c t o i n ?$ $h e l p m e . . . . . .$
	Answered by ArielVyny last updated on 31/Jul/21

	$D o m a i n : R =] - \infty; + \infty [$ $l i m i t s : l i m f {(x)}_{x \to - \infty} = {l i m}_{x \to - \infty} (x) = - \infty$ ${l i m}_{x \to + \infty} = l i m {(x - 2)}_{x \to + \infty} = + \infty$ ${l i m}_{x \to 1^{-}} l i m {(x)}_{x \to 1^{-}} = 1$ ${l i m}_{x \to 1^{+}} = l i m {(x^{2})}_{x \to 1^{+}} = 1$ ${l i m}_{x \to 3^{-}} = l i m {(x^{2})}_{x \to 3^{-}} = 9$ ${l i m}_{x \to 3^{+}} = l i m {(x - 2)}_{x \to 3^{+}} = 1$ $d e r i v a t e : \forall x < 1 f^{'} (x) = 1 o n r e m a r q u e r a f^{'} (x) n e s^{'} a n n u l e p a s$ $\forall x t e l q u e 1 ⩽ x < 3 f^{'} (x) = 2 x f^{'} (x) s^{'} a n n u l e e n 0$ $\forall x t e l q u e x ⩾ 3 f^{'} (x) = 1 f^{'} (x) n e s^{'} a n n u l e p a s$ $T a b l e a u d e v a r i a t i o n$ $\forall x t e l q u e x < 1 f (x) e s t c r o i s s a n t e (i n c r e a s e)$ $\forall x t e l q u e 1 ⩽ x < 3 f (x) e s t c r o i s s a n t e$ $\forall x t e l q u e x ⩾ 3 f (x) e s t c r o i s s a n t e$ $f (x) e s t d o n c c r o i s s a n t e s u r R p a r a i l l e u r s$ $f p r e s e n t e u n e d i s c o n t i n u i t e e n 3$ $p o i n t d e r e n c o n t r e d e l a c o u r b e a v e c l e s a x e s$ $s u r y^{'} o y o n a f (0) = 0 d o n t l a c o u r b e p a s s e p a r 0$ $s u r x^{'} o x o n a f (x) = 0 l a c o u r b e t o u c h e l^{'} a x e d e s$ $a b c i s s e s e n 0 s u r l^{'} i n t e r v a l] - \infty; 3 [$ $e n 2 s u r l^{'} i n t e r v a l e [3; + \infty [$ $j e c r o i s q u e c e s e l e m e n t p e r m e t t e n t d e t r a c e r l a c o u r b e d e c o u r b e d e f$
	Commented by saly last updated on 31/Jul/21

	$m e r c i p r o f e s s e u r!$
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