Pre-Algebra Examples

Graph log of 3(x+4)
Step 1
Find where the expression is undefined.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step 2
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
Step 3
Ignoring the logarithm, consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
Step 4
There are no horizontal asymptotes because is .
No Horizontal Asymptotes
Step 5
No oblique asymptotes are present for logarithmic and trigonometric functions.
No Oblique Asymptotes
Step 6
This is the set of all asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
Step 7