Evaluate the expression for c = –2. 11 + 7c =
2 answers:
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Solution
Asymptote:
Vertical Asymptote
- The vertical asymptotes of a rational function are determined by the denominator expression.
- The expression given is:
- The denominator of (x- 36) determines the asymptote line.
- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.
- Thus, we can say:
- Thus, the vertical asymptote is
Horizontal Asymptote:
- The horizontal asymptote exists in two cases:
1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0
2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is
- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:
End behavior:
- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.
- Thus, we have that:
Final Answers
Asymptotes:
End behavior: