Trigonometry Examples

Graph log base 4 of x-1+2
Step 1
Find the asymptotes.
Tap for more steps...
Step 1.1
Find where the expression is undefined.
Step 1.2
Since as from the left and as from the right, then is a vertical asymptote.
Step 1.3
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 1.4
There are no horizontal asymptotes because is .
No Horizontal Asymptotes
Step 1.5
No oblique asymptotes are present for logarithmic and trigonometric functions.
No Oblique Asymptotes
Step 1.6
This is the set of all asymptotes.
Vertical Asymptotes:
No Horizontal Asymptotes
Vertical Asymptotes:
No Horizontal Asymptotes
Step 2
Find the point at .
Tap for more steps...
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Tap for more steps...
Step 2.2.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1
Subtract from .
Step 2.2.1.2
Logarithm base of is .
Step 2.2.2
Add and .
Step 2.2.3
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Find the point at .
Tap for more steps...
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Tap for more steps...
Step 3.2.1
Simplify each term.
Tap for more steps...
Step 3.2.1.1
Subtract from .
Step 3.2.1.2
Logarithm base of is .
Step 3.2.2
Add and .
Step 3.2.3
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Find the point at .
Tap for more steps...
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Tap for more steps...
Step 4.2.1
Simplify each term.
Tap for more steps...
Step 4.2.1.1
Subtract from .
Step 4.2.1.2
Logarithm base of is .
Step 4.2.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.3
Combine and .
Step 4.2.4
Combine the numerators over the common denominator.
Step 4.2.5
Simplify the numerator.
Tap for more steps...
Step 4.2.5.1
Multiply by .
Step 4.2.5.2
Add and .
Step 4.2.6
The final answer is .
Step 4.3
Convert to decimal.
Step 5
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 6