Using the graph of y = h(x), as x approaches 3 from the left, the value of h(x) approaches 7. As x approaches 3 from the right, the value of h(x) approaches 7. What can you conclude about the limit of h(x) as x approaches 3?

The limit exists and is equal to 7.

Explain in your own words what it means for the limit of a function f(x) as x approaches 'a' to exist. Use the concept of approaching from both sides.

For the limit to exist, the function must approach the same value from both the left and the right side as x approaches 'a'.

Sketch a graph of a function, g(x), where the limit as x approaches 1 is equal to 4, but g(1) = 2. Explain why the limit can exist even if it is not equal to the function's value at that point.

The graph should show g(x) approaching 4 as x approaches 1 from both sides, with an open circle at (1,4) and a closed circle at (1,2). The limit describes the value the function approaches, not necessarily the actual value of the function at that point.

Consider the graph of a function k(x). As x approaches 5 from the left, k(x) approaches infinity. As x approaches 5 from the right, k(x) also approaches infinity. Does the limit of k(x) as x approaches 5 exist? Explain your reasoning.

No, the limit does not exist because the function is unbounded and approaches infinity. While both sides approach infinity, infinity is not a specific number.

Evaluating Limits Graphically

AdultMath99 min

Learning Objective

I can evaluate limits using graphing techniques.

Lesson Flow

Watch Video

7 min

Limits from graphs | Limits and continuity | AP Calculus AB | Khan Academy

Khan Academy

Guided Notes

20 min

Key concepts students will learn:

•
When evaluating limits from a graph, if the function approaches the same value from both the left and right, then the limit exists.
•
The limit of f(x) as x approaches a value can exist even if the function itself is not defined at that x-value.
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If the function approaches different values from the left and right sides of a particular x-value, then the limit does not exist.

Practice

30 min

12 questions • Multiple choice & Short answer

Exit Ticket

5 min

“Using the graph of y = h(x), what is the limit of h(x) as x approaches 3? The function is defined at h(3) = 1. As you approach x = 3 from the left, the function approaches 4. As you approach x = 3 from the right, the function approaches 4.”

Teacher Guide

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Answer keys for all questions
Differentiation strategies
Extension activities
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Evaluating Limits Graphically

Learning Objective

Lesson Flow

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Guided Notes

Practice

Exit Ticket

Teacher Guide

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