AnswersAlgebra 2 with ProbabilityGraphs of Rational Functions — QuizQuestion 6
6
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Graphs of Rational Functions — Quiz

Question 6 • Algebra 2 with Probability

f of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 6 times open paren x minus 4 close paren g of x is equal to the fraction with numerator x squared plus x plus 1 and denominator 8 times open paren x minus 4 close paren Which statement comparing the oblique asymptotes of the functions f of x and g of x is true?

Answer
A
Both functions have parallel oblique asymptotes.
B
The oblique asymptote for f of x is steeper than for g of x .
C
Both functions have the same oblique asymptote.
D
The oblique asymptote for g of x is steeper than for f of x .

Explanation

Divide the numerator by x − 4: x² + x + 1 = (x − 4)(x + 5) + 21. Thus f has oblique asymptote y = (x + 5)/6, with slope 1/6. For g, the same division gives asymptote y = (x + 5)/8, with slope 1/8. Since 1/6 is greater than 1/8, the oblique asymptote for f is steeper.

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