Classroom Resource

Introduction to Limits

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This video from Khan Academy on the CK-12 website will introduce students to the concept of limits by using two different functions as examples to demonstrate how to find the limits of a function.

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/c/calculus/concept-of-limit/lecture/Introduction-to-Limits…

Content Type / Source

CR Resource Type

Audio/Video

Resource Provider

CK-12

Accessibility

Accessibility

Video resources: includes closed captioning or subtitles

License

License Type

Custom

Custom License Type (URL)

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

Curated by

habradley

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