Exploring Rational Functions
In this activity you are going to be exploring rational functions. A rational function is a function which is the ratio of 2 polynomial functions. In this activity you will be investigating ones which are the ratio of 2 linear functions.
After you have found the values which affect a given feature (In each case it is exactly 2) and you are finding the equation of the asymptote or intercept. Then vary just those that affect it and use integer values to make it easier to spot the connection. You will have more success if you work systematically. i.e if you think c and b affect one of them, then fix b=1 say and look at different integer values of c, then fix b = 2 and do the same.
You are going to be moving the sliders a, b, c and d to see which features of the graph they affect. The 2 asymptotes and the intercepts.
Vertical Asymptote
Which vales of a, b, c and d affect the vertical asymptote?
Write the equation of the vertical asymptote in terms of a, b, c and d (in terms of the values which affect it)
Horizontal Asymptote
Which vales of a, b, c and d affect the horizontal asymptote?
Write an equation for the horizontal asymptote in terms of a, b, c and d.
y-Intercept
Which values of a, b, c and d affect the y-intercept?
Write the value of the y-intercept in terms of a, b, c and d.
x-intercept
Which values of a, b, c and d affect the x-intercept?
What is the value of the x-intercept in terms of a, b, c and d?