Lesson 7: 1-7 Selecting Procedures
Duration of Days: 2
Lesson Objective
The student will be able to:
Evaluate limits that result in infinite limits).
Connect the analytical result of a non-zero constant divided by zero to the existence of a vertical asymptote.
Select the most efficient algebraic or numerical procedure to determine a limit based on the form of the expression.
Determine the behavior of a function from the left and right of a vertical asymptote to conclude if the two-sided limit exists or is DNE.
What is the difference between an indeterminate form and an infinite limit?
How can you determine if a function is going to positive or negative infinity without looking at a graph?
Infinite Limit
Vertical Asymptote
Non-zero Constant over Zero
Unbounded Growth
Vertical Partitioning
Directional Behavior
MA.F-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Description: This lesson acts as a "sorting" lesson. Students learn to categorize limits into three results:
A Number: Found via direct substitution or simplification.
Students must check the signs of the numerator and denominator from the left and right to see if the function shoots "up" or "down.
"Purpose: This lesson prevents students from confusing "holes" with "asymptotes." It provides the logic needed to describe vertical behavior analytically, which is essential for sketching graphs and understanding function behavior in later units.
DOK Levels
DOK Level 2 (Skill/Concept): Identifying the location of vertical asymptotes by finding where the denominator is zero (but the numerator is not).DOK Level 3 (Strategic Thinking): Determining the sign of a limit (positive or negative infinity) by testing values extremely close to the asymptote.
For Struggling Students:
Mental Number Line: Have students visualize 2.999 vs 3.001 to determine if the denominator is a "tiny positive" or a "tiny negative" number.
Advanced Learners:
One-Sided Evidence: Challenge them to find a function that approaches infinity from the left of x=c and infinity from the right, explaining why the two-sided limit is simply "DNE."
AP College Board Assessments