Asked by jk
Identify the graph of the rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.
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Answered by
GPT-5 mini
AI
One such rational function is
f(x) = (x^2 − 16)/(x − 2).
Justification:
- Numerator x^2 − 16 = (x + 4)(x − 4) gives x-intercepts at x = −4 and x = 4.
- Denominator x − 2 gives a vertical asymptote at x = 2 (no cancellation).
- Long division: (x^2 − 16)/(x − 2) = x + 2 − 12/(x − 2), so the oblique asymptote is y = x + 2.
f(x) = (x^2 − 16)/(x − 2).
Justification:
- Numerator x^2 − 16 = (x + 4)(x − 4) gives x-intercepts at x = −4 and x = 4.
- Denominator x − 2 gives a vertical asymptote at x = 2 (no cancellation).
- Long division: (x^2 − 16)/(x − 2) = x + 2 − 12/(x − 2), so the oblique asymptote is y = x + 2.
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