Evaluating Limits Graphically
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Objective
I can evaluate limits using graphing techniques.
Part 1 of 4
Warm-up video
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We don't generate video — this one is by Khan Academy on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
When evaluating limits from a graph, if the function approaches the same value from both the left and right, then the limit exists.
- 2
The limit of f(x) as x approaches a value can exist even if the function itself is not defined at that x-value.
- 3
If the function approaches different values from the left and right sides of a particular x-value, then the limit does not exist.
Part 3 of 4
Practice
12 questions
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?
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.
Part 4 of 4
Exit ticket
Quick comprehension check
“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.”
Sample answer included in the free materials
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