What does it mean for a function to have a limit L as x approaches c, when determining this graphically?

It means that as the x-values get arbitrarily close to c from both the left and the right, the y-values of the function's graph get arbitrarily close to L.

Explain the relationship between one-sided limits and the existence of a two-sided limit at a particular x-value.

A two-sided limit exists if and only if both the left-hand limit and the right-hand limit exist and are equal to the same value.

Describe two different graphical scenarios where a two-sided limit at a specific x-value would not exist.

A two-sided limit does not exist if there is a jump discontinuity at that x-value, meaning the left-hand and right-hand limits are different. It also does not exist if the function approaches positive or negative infinity at that x-value, indicating a vertical asymptote.

Consider a function f(x) where the limit of f(x) as x approaches 3 is 7, but f(3) is undefined. Explain how this is possible when determining limits graphically.

This is possible if there is a hole or removable discontinuity at x=3. The graph of the function approaches a y-value of 7 from both the left and the right of x=3, but there is no actual point on the graph at x=3, meaning f(3) is undefined. The limit describes the value the function approaches, not necessarily its value at the exact point.

Finding Limits from Graphs

Name: Finding Limits from Graphs
Author: Insta~Lesson

11th Grade · Math · 40 min· Pre Calculus

Lesson Preview

Learning Objective

I can determine limits of functions graphically both one sided and two sided.

1
A limit describes the value a function approaches as its input, x, gets arbitrarily close to a specific number.
2
A two-sided limit exists if and only if both the left-hand and right-hand limits exist and are equal.
3
If a graph exhibits a jump discontinuity or a vertical asymptote, the two-sided limit at that point does not exist.

Related Lessons

No thumbnail

Subtracting Polynomials

Adding and Taking Away up to 20

Read and Write Numbers to 1,000

Related Lessons

No thumbnail

Subtracting Polynomials

Adding and Taking Away up to 20

Read and Write Numbers to 1,000

New to Insta~Lesson?

We would love to help you present Insta~Lesson to your colleagues and administrators. Here are a few resources you can use:

Finding Limits from Graphs

Lesson Preview

Learning Objective

Key Concepts

Practice Questions

Exit Ticket

Related Lessons

Subtracting Polynomials

Adding and Taking Away up to 20

Read and Write Numbers to 1,000

Related Lessons

Subtracting Polynomials

Adding and Taking Away up to 20

Read and Write Numbers to 1,000

New to Insta~Lesson?

About Insta~Lesson

How Insta~Lesson Helps Teachers Plan

How Insta~Lesson Supports Instruction Schoolwide