Asymptotes
Instructions:
f(x)=g(x)/h(x).
You may use the sliders to change the following for g(x): a, b, c, and power of g, (m), and the following for h(x): d, e, g, and power of h, (n). The asymptote(s) for f(x) will appear in the text.
Prompts:
1. Investigate Vertical Asymptote(s) of f(x). How might the vertical asymptote be obtained? What may prevent a vertical asymptote?
2. Investigate Horizontal Asymptote(s) of f(x). How might the horizontal asymptote be obtained? What is the relationship between m and n when there is a horizontal asymptote?
3. Investigate Slant Asymptote(s) of f(x). How might the slant asymptote be obtained? What is the relationship between m and n when there is a horizontal asymptote?