Classroom Resource

Concept of Limit Interactive

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This online interactive will challenge students' knowledge of limits of functions using the following scenario:

You and your friend want to understand what the definition of a limit means. Here is an informal definition of a limit.

Notation and Informal Definition of a Limit of a Function

lim f(x) = L

x→a

means that as x approaches (or gets very close to) a, the function f(x) gets very close to the value L.

In the interactive, students will move the red dots in order to manipulate the line and simulate the definition of a limit.

Content Standards

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.7
Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity.

Unpacked Content

Vocabulary

Limit
Convergent
Divergent
Continuous function
Discontinuous function
Discontinuity (infinite, jump, removable)

Knowledge

Students know:

How to graph the families of functions.
How to factor, simplify, and rationalize functions.
How to evaluate functions at a given input value.

Skills

Students are able to:

Identify continuity and discontinuity (if discontinuous, identify the type).
Calculate limits.

Understanding

Students understand that:

Functions have various types of continuity and discontinuity.
That limits can be determined numerically, graphically, and algebraically.
converging means that a limit exists, while diverging means that a limit does not exist.

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.24
Compare and contrast families of functions and their representations algebraically, graphically, numerically, and verbally in terms of their key features. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; asymptotes; and periodicity. Families of functions include but are not limited to linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, trigonometric, and their inverses.

Unpacked Content

Vocabulary

Function
Relative Maximum
Relative Minimum
Symmetry (Even/Odd)
End Behavior
Asymptotes
Intercepts
Increasing/Decreasing Intervals
Periodicity
Absolute Maximum
Absolute Minimum

Knowledge

Students know:

Properties of functions and make connections between different representations of the same function

Skills

Students are able to:

Compare properties of functions when represented in different ways (algebraically, graphically, numerically in tables or by verbal descriptions).

Understanding

Students understand that:

Each representation provides a unique perspective of the function.
Different representations are most appropriate for revealing certain key features of the function

Interdisciplinary Connection(s)

Link to Resource

https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.CAL.100.5…

Content Type / Source

CR Resource Type

Interactive/Game

Resource Provider

CK-12

Accessibility

License

License Type

Custom

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Comments or Notes

Students must create a free account online to save their progress.

Curated by

habradley

Design by Adaptive Theme