Math Problem Statement
Find the equation of the vertical asymptote f(x) = log(x + 3)
Solution
The function provided is . To find the vertical asymptote of a logarithmic function, recall that the logarithm is undefined for inputs less than or equal to zero. Therefore, the argument determines the domain of the function.
Steps:
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Solve :
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The logarithmic function is undefined at , and as , .
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Vertical Asymptote: The vertical asymptote is at:
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Related Questions:
- How do you determine the vertical asymptote for other logarithmic functions?
- What is the domain of ?
- How would the graph of look, and where is it increasing or decreasing?
- How does the shift affect the graph of the parent function ?
- Can a logarithmic function have more than one vertical asymptote?
Tip:
For logarithmic functions , always check when the argument to determine restrictions on the domain and the vertical asymptote.
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Math Problem Analysis
Mathematical Concepts
Logarithmic Functions
Vertical Asymptotes
Domain of Functions
Formulas
Vertical asymptote occurs where the argument of the logarithm is zero (x + c = 0)
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 10-12