Asymptotes might seem tricky for Year 11 students learning about rational functions.

They can cause confusion when trying to understand how graphs behave. This is especially true when it comes to spotting vertical and horizontal asymptotes.

Let’s break it down:

1. Vertical Asymptotes:

   • These show where the function goes up very high, or approaches infinity.
   • They usually happen when the bottom part of a fraction (the denominator) equals zero.

2. Horizontal Asymptotes:

   • These explain what happens to the graph as $x$ gets really big or really small (both positive and negative infinity).
   • They help us see how the graph behaves at the ends, but figuring them out can be tricky.

To overcome these challenges, students should practice finding asymptotes by looking for important points and understanding limits.

Getting a good grip on these concepts can make it easier to understand how rational functions work overall.