Ano ang mga asymptotes ng y = x / (x ^ 2-9) at paano mo i-graph ang function?

Sagot:

Ang vertical asymptotes ay # x = -3 # at # x = 3 #

Ang horizontal asymptote ay # y = 0 #

Walang pahilig na asymptote

Paliwanag:

Kailangan namin

# a ^ 2-b ^ 2 = (a + b) (a-b) #

Pinasisiya namin ang denamineytor

# x ^ 2-9 = (x + 3) (x-3) #

# y = x / ((x + 3) (x-3)) #

Tulad ng hindi namin maaaring hatiin sa pamamagitan ng #0#, x! = 3 at #x! = 3 #

Ang vertical asymptotes ay # x = -3 # at # x = 3 #

Walang mga pahilig na asymptotes bilang antas ng numerator #<# kaysa sa antas ng denamineytor

#lim_ (x -> - oo) y = lim_ (x -> - oo) x / x ^ 2 = lim_ (x -> - oo) 1 / x = 0 ^ - #

(x -> + oo) y = lim_ (x -> + oo) x / x ^ 2 = lim_ (x -> + oo) 1 / x = 0 ^ + #

Ang horizontal asymptote ay # y = 0 #

Maaari kaming bumuo ng isang tanda na tsart upang magkaroon ng pangkalahatang pananaw ng graph

#color (white) (aaaa) ## x ##color (white) (aaaa) ## -oo ##color (white) (aaaa) ##-3##color (white) (aaaaaaaa) ##0##color (white) (aaaaaaa) ##+3##color (white) (aaaaaaa) ## + oo #

#color (white) (aaaa) ## x + 3 ##color (white) (aaaa) ##-##color (white) (aaa) ##||##color (white) (aaaa) ##+##color (white) (aaaa) ##+##color (white) (aaaaa) ##||##color (white) (aaa) ##+#

#color (white) (aaaa) ## x ##color (white) (aaaaaaaa) ##-##color (white) (aaa) ##||##color (white) (aaaa) ##-##color (white) (aaaa) ##+##color (white) (aaaaa) ##||##color (white) (aaa) ##+#

#color (white) (aaaa) ## x-3 ##color (white) (aaaa) ##-##color (white) (aaa) ##||##color (white) (aaaa) ##-##color (white) (aaaa) ##-##color (white) (aaaaa) ##||##color (white) (aaa) ##+#

#color (white) (aaaa) ## y ##color (white) (aaaaaaaa) ##-##color (white) (aaa) ##||##color (white) (aaaa) ##+##color (white) (aaaa) ##-##color (white) (aaaaa) ##||##color (white) (aaa) ##+#

Ang mga intercepts ay #(0,0)#

#lim_ (x -> - 3 ^ -) y = -oo #

#lim_ (x -> - 3 ^ +) y = + oo #

#lim_ (x-> 3 ^ -) y = -oo #

#lim_ (x-> 3 ^ +) y = + oo #

Narito ang graph

graph {(y- (x) / (x ^ 2-9)) (y) (y-1000 (x + 3)) (y-1000 (x-3)) = 0 -18.05, 18.02, -9.01, 9.03}