Asked by Jaz
Which function has an asymptote at x = 39?
(1 point)
Responses
f left-parenthesis x right-parenthesis equals 7 superscript x minus 39 baseline
Image with alt text: f left-parenthesis x right-parenthesis equals 7 superscript x minus 39 baseline
f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x minus 39 right-parenthesis
Image with alt text: f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x minus 39 right-parenthesis
f left-parenthesis x right-parenthesis equals 7 superscript x plus 39 baseline
Image with alt text: f left-parenthesis x right-parenthesis equals 7 superscript x plus 39 baseline
f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x plus 39 right-parenthesis
(1 point)
Responses
f left-parenthesis x right-parenthesis equals 7 superscript x minus 39 baseline
Image with alt text: f left-parenthesis x right-parenthesis equals 7 superscript x minus 39 baseline
f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x minus 39 right-parenthesis
Image with alt text: f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x minus 39 right-parenthesis
f left-parenthesis x right-parenthesis equals 7 superscript x plus 39 baseline
Image with alt text: f left-parenthesis x right-parenthesis equals 7 superscript x plus 39 baseline
f left-parenthesis x right-parenthesis equals log subscript 7 baseline left-parenthesis x plus 39 right-parenthesis
Answers
Answered by
GPT-4o mini
To determine which function has an asymptote at \( x = 39 \), we need to analyze the given functions:
1. **\( f(x) = 7^x - 39 \)**: This function does not have a vertical asymptote at \( x = 39 \). It is an exponential function shifted vertically.
2. **\( f(x) = \log_7(x - 39) \)**: Logarithmic functions have vertical asymptotes where their arguments equal zero. Here, the asymptote occurs when \( x - 39 = 0 \), thus at \( x = 39 \).
3. **\( f(x) = 7^x + 39 \)**: Similar to the first function, this exponential function does not have an asymptote at \( x = 39 \).
4. **\( f(x) = \log_7(x + 39) \)**: This function has a vertical asymptote where \( x + 39 = 0 \), at \( x = -39 \).
From the analysis, the function that has a vertical asymptote at \( x = 39 \) is:
**\( f(x) = \log_7(x - 39) \)**.
1. **\( f(x) = 7^x - 39 \)**: This function does not have a vertical asymptote at \( x = 39 \). It is an exponential function shifted vertically.
2. **\( f(x) = \log_7(x - 39) \)**: Logarithmic functions have vertical asymptotes where their arguments equal zero. Here, the asymptote occurs when \( x - 39 = 0 \), thus at \( x = 39 \).
3. **\( f(x) = 7^x + 39 \)**: Similar to the first function, this exponential function does not have an asymptote at \( x = 39 \).
4. **\( f(x) = \log_7(x + 39) \)**: This function has a vertical asymptote where \( x + 39 = 0 \), at \( x = -39 \).
From the analysis, the function that has a vertical asymptote at \( x = 39 \) is:
**\( f(x) = \log_7(x - 39) \)**.
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