# Domain, x-intercept & Vertical Asymptote of Logarithmic Functions...1

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 16, 2021.

1. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
Section 3.2
42 & 44

Find the domain, x-intercept and vertical asymptote of each logarithmic function. Graph each function.

Note: Do 42 and 44 as a guide for me to do the rest.

nycmathguy, Oct 16, 2021
2. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
42.

Domain:
The domain of a function is the set of input or argument values for which the function is real and defined
since you have a logarithmic function, domain is

x element of R: x>0

Interval Notation:
(0,infinity )

Range:
-infinity < f(x) <infinity
Interval Notation:
(-infinity ,infinity ight)

x -intercept: => x=1

(1,0)

Asymptotes: Vertical, x=0, Horizontal: none

44.

domain:
x element of R: x>3
Interval Notation:
(3,infinity )

Range:
-infinity < h(x) <infinity
Interval Notation:
(-infinity ,infinity ight)

x-intercept: only if x=4

(4,0)

Asymptotes: Vertical, x=3, Horizontal: none

MathLover1, Oct 17, 2021
nycmathguy likes this.
3. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
1. Explain how you found the x-intercept.

2. Are you saying the domain is the argument of log function set to be > 0?

3. How did you get the range?

4. Graphing the function is the best way to determine the vertical asymptote. Yes?

nycmathguy, Oct 17, 2021
4. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
1. to find x-intercept, set f(x) to zero

log (6 ,x )=0.

2.
then write as exponential
x=6^0=> x=1
log(4,x-3)=0=>x-3=4^0 =>x-3=1 =>x=1+3=>x=4

3.
Whatever base we have for the logarithmic function, the range is always "All Real Numbers"

4. yes

MathLover1, Oct 17, 2021
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386