FINDING VERTICAL ASYMPTOTE AND DOMAIN OF LOGARITHMIC FUNCTIONS

Find the vertical asymptote, domain and key point of each of the following logarithmic functions.

Problem 1 :

f(x) = log₂(x + 5) - 3

Solution:

f(x) = log₂(x + 5) - 3

Domain:

x + 5 > 0

x > -5

Domain: (-5, ∞)

Vertical asymptote:

x + 5 = 0

x = -5

vertical asymptote x = -5

Problem 2 :

f(x) = log₅(x - 3) + 1

Solution:

f(x) = log₅(x - 3) + 1

Domain:

x - 3 > 0

x > 3

Domain: (3, ∞)

Vertical asymptote:

x - 3 = 0

x = 3

vertical asymptote x = 3

Problem 3 :

f(x) = log₃(x - 4) + 2

Solution:

f(x) = log₃(x - 4) + 2

Domain:

x - 4 > 0

x > 4

Domain: (4, ∞)

Vertical asymptote:

x - 4 = 0

x = 4

vertical asymptote x = 4

Problem 4 :

f(x) = 3log₂(x - 1) + 2

Solution:

f(x) = 3log₂(x - 1) + 2

Domain:

x - 1 > 0

x > 1

Domain: (1, ∞)

Vertical asymptote:

x - 1 = 0

x = 1

vertical asymptote x = 1

Problem 5 :

f(x) = 1/2log₄(x - 6) - 5

Solution:

f(x) = 1/2log₄(x - 6) - 5

Domain:

x - 6 > 0

x > 6

Domain: (6, ∞)

Vertical asymptote:

x - 6 = 0

x = 6

vertical asymptote x = 6

Problem 6 :

f(x) = -4log₂(x - 2)

Solution:

f(x) = -4log₂(x - 2)

Domain:

x - 2 > 0

x > 2

Domain: (2, ∞)

Vertical asymptote:

x - 2 = 0

x = 2

vertical asymptote x = 2