ALEX | Alabama Learning Exchange

More Graphs of Functions

Classroom Resource Information

Title:

More Graphs of Functions

URL:

https://aptv.pbslearningmedia.org/resource/our20-math-855/more-graphs-of-functions/

Content Source:

PBS

Type:

Audio/Video

Overview:

In this video lesson, students begin to analyze graphs of functions and use them to answer questions about a context. Students look at what happens over intervals of input values and learn that graphs can be viewed as dynamic objects that tell stories. They connect specific features of the graph with specific features of the contextual situation and investigate what happens over ranges of input values. As students learn to interpret graphs in terms of a context and use them to answer questions, they learn an important skill in mathematical modeling (MP4).

Grade 8, Episode 9: Unit 5, Lesson 5 | Illustrative Math

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 8

13. Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.

Unpacked Content

Evidence Of Student Attainment:

Students:

Define a function as a rule assigning each input exactly one output.
Identify functions when given a relation as graph, table of values, mapping, or set of ordered pairs.

Teacher Vocabulary:

Relation
Function
Input
Output

Knowledge:

Students know:

how to interpret a graph, table, mapping, and ordered pairs.

Skills:

Students are able to:

give an accurate definition of a function.
Analyze graphs, tables, mappings, and sets of ordered pairs to determine if a relation is a function.

Understanding:

Students understand that:

Functions assign every input one output, but they may see outputs repeat.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.13.1: Define function, ordered pairs, input, output.
M.8.13.2: Demonstrate how to plot points on a Cartesian plane using ordered pairs.
M.8.13.3: Recall how to complete input/output tables.
M.8.13.4: Recognize numeric patterns.
M.8.13.5: Given a function, create a rule.

Prior Knowledge Skills:

Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
Demonstrate an understanding of an extended coordinate plane.
Draw a four-quadrant coordinate plane.
Draw and extend vertical and horizontal number lines.
Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
Recall how to graph points in all four quadrants of the coordinate plane.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.8.13 Determine whether a relation is a function given a graph or a table.

Mathematics
MA2019 (2019)
Grade: 8
Accelerated

16. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. [Grade 8, 13, edited for added content]

a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [Grade 8, 14, edited for added content]
Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions. [Algebra I with Probability, 15]

Unpacked Content

Evidence Of Student Attainment:

Students:
Given a functional relationship,

Determine that exactly one element of the range (output) is assigned to each element of the domain (input) by the function,
Represent the function with a graph and with functional notation.
Evaluate functional notation to produce a range when given a value in the domain,
Explain in the original context the meaning of the output when related to the input.

Given a contextual situation that is functional,

Model the situation with a graph and construct the graph based on the parameters given in the domain of the context.
Distinguish between those that are functions and non-functions.

Teacher Vocabulary:

Function
Relation
Mapping
Domain
Range
Functional notation f(x)
Element
Input
output
Quantitative relationship

Knowledge:

Students know:

Distinguishing characteristics of functions,
Conventions of function notation,
Techniques for graphing functions,
Techniques for determining the domain of a function from its context.

Skills:

Students are able to:

Accurately graph functions when given function notation.
Accurately evaluate function equations given values in the domain.
Interpret the domain from the context,
Produce a graph of a function based on the context given.

Understanding:

Students understand that:

Functions are relationships between two variables that have a unique characteristic: that for each input there exists exactly one output.
Function notation is useful to see the relationship between two variables when the unique output for each input relation is satisfied.
Different contexts produce different domains and graphs.
Function notation in itself may produce graph points which should not be in the graph as the domain is limited by the context.

Diverse Learning Needs:

Tags:

functions, graphs, input, output, tables

License Type:

Custom Permission Type
See Terms: https://aptv.pbslearningmedia.org/help/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Video resources: includes closed captioning or subtitles

Comments

Additional activity and practice pages are provided for this video lesson.

This resource provided by:

Author:

Kristy Lacks

ALEX Classroom Resource

More Graphs of Functions