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Flip to reveal answersWhere is the vertical asymptote of (ax + b)/(cx + d)?
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All 9 Flashcards — Rational functions
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Question
Where is the vertical asymptote of (ax + b)/(cx + d)?
Answer
Where the denominator is zero: cx + d = 0.
Question
Where is the horizontal asymptote of (ax + b)/(cx + d)?
Answer
y = a/c — the ratio of the leading coefficients.
Question
Where is the x-intercept of a rational function?
Answer
Where the numerator = 0 (a fraction is zero only when its top is zero).
Question
Where is the y-intercept of (ax + b)/(cx + d)?
Answer
At x = 0: y = b/d.
Question
Vertical asymptote of y = (2x + 1)/(x − 4)?
Answer
x = 4 (denominator zero).
Question
Horizontal asymptote of y = (2x + 1)/(x − 4)?
Answer
y = 2 (leading coefficients 2/1).
Question
Why is the horizontal asymptote a/c?
Answer
Dividing top and bottom by x, the b and d terms vanish, leaving a/c.
Question
How many vertical asymptotes does (ax + b)/(cx + d) have?
Answer
One — the linear denominator has a single zero.
Question
How do you sketch a rational function?
Answer
Draw the asymptotes, plot the x- and y-intercepts, then draw the two branches.
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Full study notes for Rational functions
Topic 2.8 hub
Rational functions & asymptotes
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