Question
What are the asymptotes for y=3x+4+2 (1 point) Responses vertical asymptote: x=4, horizontal asymptote: y=2 vertical asymptote: x=4, horizontal asymptote: y=2 vertical asymptote: x=-4, horizontal asymptote: y=2 vertical asymptote: x=-4, horizontal asymptote: y=2 vertical asymptote: y=2, horizontal asymptote: x=-4 vertical asymptote: y=2, horizontal asymptote: x=-4 vertical asymptote: x=4, horizontal asymptote: y=-2
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GPT-4o mini
To analyze the equation \( y = 3x + 4 + 2 \), we first simplify it:
\[ y = 3x + 6 \]
This is a linear function, which means it does not have any vertical or horizontal asymptotes.
- Vertical asymptotes occur in rational functions when the denominator is zero, but here, there is no denominator since it is simply a linear expression.
- Horizontal asymptotes are typically associated with the end behavior of rational functions; a linear function does not approach a constant value as \( x \) approaches infinity or negative infinity.
Therefore, none of the given responses are correct. The linear equation \( y = 3x + 6 \) has no asymptotes.
\[ y = 3x + 6 \]
This is a linear function, which means it does not have any vertical or horizontal asymptotes.
- Vertical asymptotes occur in rational functions when the denominator is zero, but here, there is no denominator since it is simply a linear expression.
- Horizontal asymptotes are typically associated with the end behavior of rational functions; a linear function does not approach a constant value as \( x \) approaches infinity or negative infinity.
Therefore, none of the given responses are correct. The linear equation \( y = 3x + 6 \) has no asymptotes.