First, students will learn how to evaluate a limit graphically, when the limit exists.

Watch these videos:

- Introduction to Limits by NancyPi
- Estimating limit values from graphs by Khan Academy

Next, students will learn to recognize when a functions value is approaching positive or negative infinity, from either side, and what it tells us about the limit at that asymptote.

Unbounded limits by Khan Academy

After that, students will practice both skills.

Estimating limit values from graphs by Khan Academy

Next, students will learn how to evaluate a one-sided limit graphically, when the limit exists.

One-sided limits from graphs by Khan Academy

After that, students will learn to recognize when a functions value is approaching positive or negative infinity, from one side, and what it tells us about the one-sided limit at that asymptote.

One-sided limits from graphs: asymptote by Khan Academy

After that, students will practice both skills.

After that, students will learn how to evaluate more complicated limits graphically.

Ex 1: Determine Limits from a Graph Using Function Notation by Mathispower4u

Next, students will learn that a limit only tells us about the values around a point. For any limit, we could construct infinitely many functions which have that limit in common. Students will also learn that we needn't always take the limit at points of discontinuity, or at asymptotes. We also needn't take the limit at integer values, we could take the limit of \(f(x)\) as \(x\) approaches \(\pi,\) for example.

Connecting limits and graphical behavior by Khan Academy

Connecting limits and graphical behavior by Khan Academy

Conclude by giving your students these challenges: