Practice question · Select all that apply
Let . Select every TRUE statement about its graph.
Hints
- Vertical asymptotes come from zeros of the denominator; x-intercepts from zeros of the numerator.
- For the horizontal asymptote, divide numerator and denominator by x and let x grow.
Show the answer
- A. The x-intercept is at x = -1
- B. There is a vertical asymptote at x = 3
- D. The y-intercept is -1/3
- E. The horizontal asymptote is the line y = 1
Why
f(0) = 1/(-3) = -1/3 and the numerator vanishes at -1. As x grows, (x + 1)/(x - 3) tends to 1, not 0, the numerator and denominator have equal degree, so the ratio of leading coefficients gives the asymptote. Assuming every rational function flattens to y = 0 is the usual error.
Practise Curve Sketching
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