ALEX Classroom Resource

  

Algebra I Module 3, Topic B: Functions and Their Graphs

  Classroom Resource Information  

Title:

 Algebra I Module 3, Topic B: Functions and Their Graphs

URL:

 https://www.engageny.org/resource/algebra-i-module-3-topic-b-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 3, Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and interpret functions in abstract and contextual situations (F-IF.A.1, F-IF.A.2). Students examine the graphs of a variety of functions and learn to interpret those graphs using precise terminology to describe such key features as domain and range, intercepts, intervals where the function is increasing or decreasing, and intervals where the function is positive or negative. (F-IF.A.1, F-IF.B.4, F-IF.B.5, F-IF.C.7a).

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
26 ) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [F-IF2]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.F.HS.26- Substitute x-values into one-step linear equations in two variables (y = x + p or y = px) and solve for the y-values. (this could include the original information listed above and have students represent in data table)
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
15. 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.

a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 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.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given input/output relations between two variables in graphical form, verbal description, set of ordered pairs, or algebraic model, distinguish between those that are functions and non-functions.


Using functional notation,
  • Evaluate functions for inputs.
  • Interpret statements in terms of context.


Given a contextual relationship that may be represented as a function,
  • Determine that exactly one element of the range (output) is assigned to each element of the domain (input) by the function.
  • Relate the domain to its graph and to the quantitative relationship it describes.
Teacher Vocabulary:
  • Domain
  • Range
  • Function
  • Relation
  • Function notation
  • Set notation
Knowledge:
Students know:
  • Distinguishing characteristics of functions.
  • Conventions of function notation.
  • In graphing functions the ordered pairs are (x,f(x)) and the graph is y = f(x).
Skills:
Students are able to:
  • Evaluate functions for inputs in their domains.
  • Interpret statements that use function notation in terms of context.
  • Accurately graph functions when given function notation.
  • Accurately determine domain and range values from function notation.
Understanding:
Students understand that:
  • A function is a mapping of the domain to the rangeFunction notation is useful in contextual situations to see the relationship between two variables when the unique output for each input relation is satisfied.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.15.1: Define domain, range, relation, function, table of values, input, and output.
ALGI.15.2: Understand the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
ALGI.15.3: Understand that a function is a rule that assigns to each input exactly one output.
ALGI.15.4: Identify the equation of a function, given its graph.
ALGI.15.5: Find the range of a function given its domain.
ALGI.15.6: Recognize that f(x) and y are the same.
ALGI.15.7: Recall how to complete input/output tables.
ALGI.15.8: Recall how to read/interpret information from a table.
ALGI.15.9: Define function notation.
ALGI.15.10: Translate a simple word problem into function notation.
ALGI.15.11: Evaluate function when given x-value.

Prior Knowledge Skills:
  • Analyze the graph to determine the rate of change.
  • Generate the slope of a line using given ordered pairs.
  • Define linear functions, nonlinear functions, slope, and y-intercept
  • Identify ordered pairs.
  • Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.15 Use the vertical line test to determine if a given relation is a function.
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a function that models a relationship between two quantities, produce the graph and table of the function and show the key features (intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity) that are appropriate for the function.


Given key features from verbal description of a relationship,
  • Sketch a graph with the given key features.
  • Know periodicity.
Teacher Vocabulary:
  • Function
  • Periodicity
  • x-intercepts
  • y-intercepts
  • Intervals of Increasing
  • Intervals of decreasing
  • Function is positive
  • Function is negative
  • Relative Maximum
  • Relative Minimum
  • y-axis symmetry
  • Origin symmetry
  • End behavior
Knowledge:
Students know:
  • Key features of function graphs (i.e., intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity).
  • Methods of modeling relationships with a graph or table.
Skills:
Students are able to:
  • Accurately graph any relationship.
  • Interpret key features of a graph.
Understanding:
Students understand that:
  • The relationship between two variables determines the key features that need to be used when interpreting and producing the graph.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.28.1: Define intercepts, intervals, relative maxima, relative minima, symmetry, end behavior, and periodicity.
ALGI.28.2: For a function that models a relationship between two quantities, find the periodicity.
ALGI.28.3: For a function that models a relationship between two quantities, find the end behavior.
ALGI.28.4: For a function that models a relationship between two quantities, find the symmetry.
ALGI.28.5: For a function that models a relationship between two quantities, find the intervals where the function is increasing, decreasing, positive, or negative.
ALGI.28.6: For a function that models a relationship between two quantities, find the relative maxima and minima.
ALGI.28.7: For a function that models a relationship between two quantities, find the x and y intercepts.

Prior Knowledge Skills:
  • Identify parts of the Cartesian plane.
  • Graph a function given the slope-intercept form of an equation.
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from table.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.28 Given graphs that represent linear functions, identify key features (limit to y intercept, x-intercept, increasing, decreasing) and/or interpret different rates of change (e.g., Which is faster or slower?).
Tags: domain, evaluate, function, graphs, inputs, intercepts, intervals, range, tables
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There are seven lessons on this topic.

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Author: Hannah Bradley
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