Respuestas
Para f(x) = 1 / (x-3):
Las asíntotas verticales son los valores que indefinen el denominador. Esto es:
x - 3 = 0
x = 3 → Asíntota vertical
y = 0 → Asíntota horizontal
Valores Tabulares:
-4 f(-4) = 1/(-4 - 3) = -0.1429
-3 f(-3) = 1/(-3 - 3) = -0.1667
-2 f(-2) = 1/(-2 - 3) = -0.2
-1 f(-1) = 1/(-1 - 3) = -0.25
0 f(0) = 1/(0 - 3) = -0.3333
1 f(1) = 1/(1 - 3) = -0.5
2 f(2) = 1/(2 - 3) = -1.0
4 f(4) = 1/(4 - 3) = 1.0
5 f(5) = 1/(5 - 3) = 0.5
6 f(6) = 1/(6 - 3) = 0.3333
7 f(7) = 1/(7 - 3) = 0.25
8 f(8) = 1/(8 - 3) = 0.2
9 f(9) = 1/(9 - 3) = 0.1667
Para f(x) = x / (x²-4):
Las asíntotas verticales son los valores que indefinen el denominador. Esto es:
x²-4 = 0
x = ± 2 → asíntotas verticales
Valores Tabulares:
-6 f(-6) = -6/((-6)² - 3) = -0.1875
-5 f(-5) = -5/((-5)² - 3) = -0.2381
-4 f(-4) = -4/((-4)² - 3) = -0.3333
-3 f(-3) = -3/((-3)² - 3) = -0.6
-1 f(-1) = -1/((-1)² - 3) = 0.3333
0 f(0) = 0/((0)² - 3) = 0
1 f(1) = 1/((1)² - 3) = -0.3333
3 f(3) = 3/((3)² - 3) = 0.6
4 f(4) = 4/((4)² - 3) = 0.3333
5 f(5) = 5/((5)² - 3) = 0.2381
6 f(6) = 6/((6)² - 3) = 0.1875
Para f(x) = √x
0 f(0) = √0 = 0.0
1 f(1) = √1 = 1.0
2 f(2) = √2 = 1.4142
3 f(3) = √3 = 1.7321
4 f(4) = √4 = 2.0
5 f(5) = √5 = 2.2361
6 f(6) = √6 = 2.4495
7 f(7) = √7 = 2.6458
* Las raíces de números negativos no están definidas siendo el dominio de la función x ≥ 0.
* No hay asíntotas
Para f(x) = √-x
-10 f(-10) = √-(-10) = 3.1623
-9 f(-9) = √-(-9) = 3.0
-8 f(-8) = √-(-8) = 2.8284
-7 f(-7) = √-(-7) = 2.6458
-6 f(-6) = √-(-6) = 2.4495
-5 f(-5) = √-(-5) = 2.2361
-4 f(-4) = √-(-4) = 2.0
-3 f(-3) = √-(-3) = 1.7321
-2 f(-2) = √-(-2) = 1.4142
-1 f(-1) = √-(-1) = 1.0
0 f(0) = √-0 = 0.0
* No hay asíntotas
f(x) =2^(x)+1
-3 f(-3) =2^(-3)+1 = 1.125
-2 f(-2) =2^(-2)+1 = 1.25
-1 f(-1) =2^(-1)+1 = 1.5
0 f(0) =2^(0)+1 = 2
1 f(1) =2^(1)+1 = 3
2 f(2) =2^(2)+1 = 5
3 f(3) =2^(3)+1 = 9
Asíntota horizontal: y = 1 (El término independiente es la asíntota en una función exponencial)
f(x) =½^(x)+1
-3 f(-3) =½^(-3)-1 = 7.0
-2 f(-2) =½^(-2)-1 = 3.0
-1 f(-1) =½^(-1)-1 = 1.0
0 f(0) =½^(0)-1 = 0.0
1 f(1) =½^(1)-1 = -0.5
2 f(2) =½^(2)-1 = -0.75
3 f(3) =½^(3)-1 = -0.875
Asíntota horizontal: y = -1 (El término independiente es la asíntota en una función exponencial)
f(x) =log₂(x)+1
0.4 f(0.4) =log₂ (0.4)+1 = -0.3219
0.8 f(0.8) =log₂ (0.8)+1 = 0.6781
1.2 f(1.2) =log₂ (1.2)+1 = 1.263
1.6 f(1.6) =log₂ (1.6)+1 = 1.6781
2.0 f(2.0) =log₂ (2.0)+1 = 2.0
2.4 f(2.4) =log₂ (2.4)+1 = 2.263
2.8 f(2.8) =log₂ (2.8)+1 = 2.4854
3.2 f(3.2) =log₂ (3.2)+1 = 2.6781
3.6 f(3.6) =log₂ (3.6)+1 = 2.848
El logaritmo no se define para x≤0 por tanto x = 0 es una asíntota vertical.
f(x) = 2log₃ (x)+2
0.2 f(0.2) =2log₃ (0.2)+2 = -0.9299
0.4 f(0.4) =2log₃ (0.4)+2 = 0.3319
0.6 f(0.6) =2log₃ (0.6)+2 = 1.0701
0.8 f(0.8) =2log₃ (0.8)+2 = 1.5938
1.0 f(1.0) =2log₃ (1.0)+2 = 2.0
1.2 f(1.2) =2log₃ (1.2)+2 = 2.3319
1.4 f(1.4) =2log₃ (1.4)+2 = 2.6125
1.6 f(1.6) =2log₃ (1.6)+2 = 2.8556
1.8 f(1.8) =2log₃ (1.8)+2 = 3.0701
El logaritmo no se define para x≤0 por tanto x = 0 es una asíntota vertical.
f(x)= 2sen(x)+1
0 f(0)= 2sen(0°)+1 = 1.0
30 f(30)= 2sen(30°)+1 = 2.0
60 f(60)= 2sen(60°)+1 = 2.7321
90 f(90)= 2sen(90°)+1 = 3.0
120 f(120)= 2sen(120°)+1 = 2.7321
150 f(150)= 2sen(150°)+1 = 2.0
180 f(180)= 2sen(180°)+1 = 1.0
210 f(210)= 2sen(210°)+1 = 0
240 f(240)= 2sen(240°)+1 = -0.7321
270 f(270)= 2sen(270°)+1 = -1.0
300 f(300)= 2sen(300°)+1 = -0.7321
330 f(330)= 2sen(330°)+1 = 0
360 f(350)= 2sen(350°)+1 = 0.6527
Asíntotas horizontales y = 3 y y = -1.
f(x)= 2cos(x)+1
0 f(0)= 2cos(0°)+1 = 3.0
30 f(30)= 2cos(30°)+1 = 2.7321
60 f(60)= 2cos(60°)+1 = 2.0
90 f(90)= 2cos(90°)+1 = 1.0
120 f(120)= 2cos(120°)+1 = 0.0
150 f(150)= 2cos(150°)+1 = -0.7321
180 f(180)= 2cos(180°)+1 = -1.0
210 f(210)= 2cos(210°)+1 = -0.7321
240 f(240)= 2cos(240°)+1 = -0.0
270 f(270)= 2cos(270°)+1 = 1.0
300 f(300)= 2cos(300°)+1 = 2.0
330 f(330)= 2cos(330°)+1 = 2.7321
360 f(350)= 2cos(350°)+1 = 2.9696
Asíntotas horizontales y = 3 y y = -1.
