From previous courses, we've gained the notion of horizontal asymptotes. When we have a function with the following graph:
we notice that the graph is basically zero as we look further to the left or right. Since the graph approaches zero for larger \(x\)-values, we say that the horizontal asymptote of \(f(x)\) is \(y=0\).
Let's observe the behavior of \( f(x) = x^2 - 2x + 2 \) as \( x \) approaches a specific value \( a \).
Homework: Find the limit of \( f(x) = x^2 \) as \( x \to 2 \).