Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = 0 en dus is y = 0;
The horizontal asymptote : q = 0 and therefore y =0.
a = 4 en dus positief sodat die kromme in
kwadrante I en III lê.
a = 4 and thus positive so that the curve is in
quadrants I and III
x = 0 en y = 0 sodat daar geen afsnitte op
die asse is nie.
x = 0 and y = 0 so that there are no intercepts
on the axes.
Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = 0 en dus is y = 0;
The horizontal asymptote : q = 0 and therefore y =0.
a = −6 en dus negatief sodat die kromme in
kwadrante II en IV lê.
a = −6 and thus negative so that the curve is in
quadrants II and IV
x = 0 en y = 0 sodat daar geen afsnitte op
die asse is nie.
x = 0 and y = 0 so that there are no intercepts
on the axes.
Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = 1 en dus is y = 1;
The horizontal asymptote : q = 1 and therefore y = 1.
a = 2 en dus positief sodat die kromme in
kwadrante I en III lê.
a = 2 and thus positive so that the curve is in
quadrants I and III
2
X-afsnit / X-intercept : 0 = — + 1
x
X x :
0 = 2 + x
−2 = x
X-afsnit / X-intercept is A (−2 ; 0)
Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = −3 en dus is y = −3
The horizontal asymptote : q = −3 and therefore y = −3
a = 6 en dus positief sodat die kromme in
kwadrante I en III lê.
a = 6 and thus positive so that the curve is in
quadrants I and III
6
X-afsnit / X-intercept :
0 = — − 3
x
X x :
0 = 6 − 3x
3x = 6
x = 2
X-afsnit / X-intercept is A (2 ; 0)
Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = 5 en dus is y = 5
The horizontal asymptote : q = 5 and therefore y = 5
a = −8 en dus positief sodat die kromme in
kwadrante II en IV lê.
a = −8 and thus positive so that the curve is in
quadrants II and IV
8
X-afsnit / X-intercept :
0 = 5 − —
x
X x :
0 = 5x − 8
5x = 8
x = 8/5 = 1,6
X-afsnit / X-intercept is A (1,6 ; 0)
Die vertikale asimptoot : x = 0
The vertical asymptote : x = 0
Die horisontale asimptoot : q = 4 en dus is y = 4
The horizontal asymptote : q = 4 and therefore y = 4
a = −2 en dus positief sodat die kromme in
kwadrante II en IV lê.
a = −2 and thus positive so that the curve is in
quadrants II and IV
2
X-afsnit / X-intercept :
0 = 4 − —
x
X x :
0 = 4x − 2
2 = 4x
x = 2/4 = 0,5
X-afsnit / X-intercept is A (0,5 ; 0)
Vertikale asimptoot / Vertical asymptote : x = 0
Horisontale asimptoot / Horizontal asymptote : y = 0
a
Vergelyking / Equation : y = —
x
a
By / At A(2;4) :
4 = —
2
X 2 : 8 = a
8
Vergelyking / Equation : y = —
x
Horisontale asimptoot / Horizontal asymptote : x = 0
Vertikale asimptoot / Vertical asymptote : y = 0
a
Vergelyking / Equation : y = —
x
a
By / At B(−3;4) :
4 = ——
−3
X −3 : −12 = a
−12
Vergelyking / Equation : y = ———
x
Vertikale asimptoot / Vertical asymptote : x = 0
Horisontale asimptoot / Horizontal asymptote : y = 1
Horisontale asimptoot / Horizontal asymptote ∴ q = 1
a
Vergelyking / Equation : y = — + 1
x
a
By / At P(1;3) :
3 = — + 1
1
X 1 : 3 = a + 1
2 = a
2
Vergelyking / Equation : y = — + 1
x
Vertikale asimptoot / Vertical asymptote : x = 0
Horisontale asimptoot / Horizontal asymptote : y = −3
Horisontale asimptoot / Horizontal asymptote ∴ q = −3
a
Vergelyking / Equation : y = — − 3
x
a
By / At P(1;4) :
4 = —— − 3
1
X 1 : 4 = a − 3
7 = a
7
Vergelyking / Equation : y = — − 3
x
Antwoord / Answer 3.
3.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = 1
∴
q = 1
a
3.2 Vergelyking / Equation : y = — + 1
x
a
By / At P(3;2) :
2 = —— + 1
3
X 3 : 6 = a + 3
3 = a
3
Vergelyking / Equation : y = — + 1
x
3
3.3 Vergelyking / Equation : y = — + 1
x
3
X-afsnit / X-intercept :
0 = —— + 1
x
X x : 0 = 3 + x
−3 = x
X-afsnit / X-intercept A is (−3 ; 0)
3
3.4 Vergelyking / Equation : y = — + 1
x
3
By / At B(b;4) :
4 = —— + 1
b
X b : 4b = 3 + b
3b = 3
b = 1
3
3.5 Vergelyking / Equation : y = — + 1
x
3
By / At C(−1;c) :
c = —— + 1
−1
c = −3 + 1
c = −2
3.6 Definisieversameling / Domain
{ x | x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ 1; y ∈ ℜ }
Vraag / Question 3.
Antwoord / Answer 4.
4.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = −2
∴
q = −2
a
4.2 Vergelyking / Equation : y = — − 2
x
a
By / At R(2;−4) :
−4 = —— − 2
2
X 2 : −8 = a − 4
−4 = a
−4
Vergelyking / Equation : y = —— − 2
x
−4
4.3 Vergelyking / Equation : y = —— − 2
x
−4
X-afsnit / X-intercept :
0 = —— − 2
x
X x : 0 = −4 − 2x
−2 = x
X-afsnit / X-intercept A is (−2 ; 0)
−4
4.4 Vergelyking / Equation : y = —— − 2
x
−4
By / At Q(−3;t) :
t = —— − 2
X −3 : −3t = −4 + 6
3t = −2
−2
t = ——
3
−4
4.5 Vergelyking / Equation : y = —— − 2
x
−4
By / At R(r;−4) :
−4 = —— − 2
r
X r : −4r = −4 − 2r
−2r = −4
r = 2
4.6 Definisieversameling / Domain
{ x | x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ −2; y ∈ ℜ }
Vraag / Question 4.
Antwoord / Answer 5.
5.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = 3
∴
q = 3
a
5.2 Vergelyking / Equation : y = — + 3
x
−5
X-afsnit / X-intercept :
0 = —— + 3
x
X x : 0 = −5 + 3x
5 = 3x
5
— = x
3
5
X-afsnit / X-intercept A is (— ; 0)
3
−5
5.3 Vergelyking / Equation : y = —— + 3
x
−5
By / At B(b;−2) :
−2 = —— + 3
b
X b : −2b = −5 + 3b
−5b = −5
b = 1
−5
5.4 Vergelyking / Equation : y = —— + 3
x
−5
By / At C(2;c) :
c = —— + 3
2
X 2 : 2c = −5 + 6
2c = 1
1
c = ——
2
5.5
. Definisieversameling / Domain
{ x | x ≠ 0; x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ 3; y ∈ ℜ }
Antwoord / Answer 6.
6.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = −5
∴
q = −5
−6
6.2 Vergelyking / Equation : y = —— − 5
x
−6
X-afsnit / X-intercept :
0 = —— − 5
x
X x : 0 = −6 − 5x
5x = −6
−6
x = ——
5
−6
X-afsnit / X-intercept A is (—— ; 0)
5
−6
6.3 Vergelyking / Equation : y = —— − 5
x
−6
By / At B(b;3) :
3 = —— − 5
b
X b : 3b = −6 − 5b
8b = −6
−3
b = ——
4
−6
6.4 Vergelyking / Equation : y = —— − 5
x
−6
By / At C(2;c) :
c = —— − 5
2
X 2 : 2c = −6 − 10
2c = −16
c = −8
6.5
. Definisieversameling / Domain
{ x | x ≠ 0; x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ −5; y ∈ ℜ }
Antwoord / Answer 7.
7.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = −5
∴
q = −5
a
7.2 Vergelyking / Equation : y = — − 5
x
a
By / At P(0,5;3) :
3 = —— − 5
0,5
X 0,5 : 1,5 = a − 2,5
4 = a
4
Vergelyking / Equation : y = —— − 5
x
4
7.3 Vergelyking / Equation : y = —— − 5
x
4
X-afsnit / X-intercept :
0 = —— − 5
x
X x : 0 = 4 − 5x
5x = 4
4
x = —
5
X-afsnit / X-intercept A is (0,8 ; 0)
4
7.4 Vergelyking / Equation : y = —— − 5
x
4
By / At B(b;−3) :
−3 = —— − 5
b
X b : −3b = 4 − 5b
2b = 4
b = 2
4
7.5 Vergelyking / Equation : y = —— − 5
x
4
By / At C(−1,6;c) :
c = —— − 5
−1,6
X −1,6 : −1,6c = 4 + 8
−1,6c = 12
c = −7,5
7.6 Definisieversameling / Domain
{ x | x ≠ 0; x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ −5; y ∈ ℜ }
Vraag / Question 7.
Antwoord / Answer 8.
8.1 Vertikale asimptoot / Vertical asymptote
:
x = 0
Horisontale asimptoot / Horizontal asymptote
: y = −3
∴
q = −3
a
8.2 Vergelyking / Equation : y = — − 3
x
a
By / At P(4;−3,5) :
−3,5 = —— − 3
4
X 4 : −14 = a − 12
−2 = a
2
Vergelyking / Equation : y = − —— − 3
x
2
8.3 Vergelyking / Equation : y = − —— − 3
x
2
X-afsnit / X-intercept :
0 = − —— − 3
x
X x : 0 = −2 − 3x
3x = −2
−2
x = —
3
−2
X-afsnit / X-intercept A is (—— ; 0)
3
2
8.4 Vergelyking / Equation : y = —— − 3
x
2
By / At B(2;b) :
b = —— − 3
2
b = 1 − 3
b = −2
2
8.5 Vergelyking / Equation : y = —— − 3
x
2
By / At C(c;−1) :
−1 = —— − 3
c
X c : −c = 2 − 3c
2c = 2
c = 1
8.6 Definisieversameling / Domain
{ x | x ≠ 0; x ∈ ℜ }
Waardeversameling / Range
{ y | y ≠ −3; y ∈ ℜ }
Vraag / Question 8.