Asymptotes and Limits of Functions
Directions: Use the applet below to explore the relationships between asymptotes and as x → ∞, discover what f(x) goes towards. Begin by inputting a function in the input box (where it says f(x)=). Slide the point A on the graph left or right along the x-axis to make the x values grow larger and smaller, and observe how the y-values react. Feel free to zoom out on the graph to get larger values for x. Use the check-box to show the equations for the asymptotes and graph them on the graph.
Consider the following questions as you explore:
#1. As x → ∞ (this means the x-values get larger and larger- big enough to the point we don't want to count them anymore), what does f(x) or the y-values approach?
#2. As x → -∞ (this means the x-values get larger and larger- big enough to the point we don't want to count them anymore), what does f(x) or the y-values approach?
#3. How do the asymptotes (specifically the horizontal asymptotes) relate to parts #1 and #2?