Find the equation of vertical asymptote :
1. f(x) = 1/(x + 6)
2. f(x) = (x^{2} + 2x - 3)/(x^{2} - 5x + 6)
3. f(x) = (2x - 3)/(x^{2} - 4)
4. f(x) = (2x - 3)/(x^{2} + 4)
1. Answer :
f(x) = 1/(x + 6)
Step 1 :
In the given rational function, the denominator is
x + 6
Step 2 :
Equate the denominator to zero and solve for x.
x + 6 = 0
x = - 6
Step 3 :
The equation of the vertical asymptote is
x = - 6
2. Answer :
f(x) = (x^{2} + 2x - 3)/(x^{2} - 5x + 6)
Step 1 :
In the given rational function, the denominator is
x^{2} - 5x + 6
Step 2 :
Equate the denominator to zero and solve for x.
x^{2} - 5x + 6 = 0
(x - 2)(x - 3) = 0
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3
Step 3 :
The equations of two vertical asymptotes are
x = 2 and x = 3
3. Answer :
f(x) = (2x - 3)/(x^{2} - 4)
Step 1 :
In the given rational function, the denominator is
x^{2} - 4
Step 2 :
Equate the denominator to zero and solve for x.
x^{2} - 4 = 0
x^{2} - 2^{2} = 0
(x + 2)(x - 2) = 0
x = -2 or x = 2
Step 3 :
The equations of two vertical asymptotes are
x = -2 and x = 2
4. Answer :
f(x) = (2x - 3)/(x^{2} + 4)
Step 1 :
In the given rational function, the denominator is
x^{2} + 4
Step 2 :
Equate the denominator to zero and solve for x.
x^{2} + 4 = 0
x^{2} = -4
x = ±√-4
x = ±2i
x = 2i or x = -2i (Imaginary)
Step 3 :
When we equate the denominator to zero, we don't get real values for x.
So, there is no vertical asymptote.
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