To determine the vertical and horizontal asymptotes of the function [tex]\( f(x) = x - 1 \)[/tex], we need to analyze its behavior.
### Vertical Asymptotes:
Vertical asymptotes are found by identifying values of [tex]\( x \)[/tex] that make the denominator of a rational function equal to zero. Since [tex]\( f(x) = x - 1 \)[/tex] is a linear function and not a rational function (it has no denominator that could be zero), it does not have any vertical asymptotes.
### Horizontal Asymptotes:
Horizontal asymptotes are determined by analyzing the end behavior of the function as [tex]\( x \)[/tex] approaches infinity or negative infinity.
- As [tex]\( x \to \infty \)[/tex], [tex]\( f(x) = x - 1 \to \infty \)[/tex].
- As [tex]\( x \to -\infty \)[/tex], [tex]\( f(x) = x - 1 \to -\infty \)[/tex].
Since the function grows without bound (both positively and negatively) as [tex]\( x \)[/tex] moves away from zero, there are no horizontal asymptotes.
### Conclusion:
Based on the above analysis:
- Vertical asymptotes: None
- Horizontal asymptotes: None
None of the provided options match our findings. Therefore, the correct conclusion is that there are no vertical or horizontal asymptotes for the function [tex]\( f(x) = x - 1 \)[/tex].
