Students are introduced to the main features of functions that they will learn throughout the year, providing students with a conceptual understanding of how functions are used to model various situations.
In Unit 1, Functions, Graphs, and Features, students are introduced to all of the main features of functions they will learn throughout the year through basic graphical modeling of contextual situations. Students will learn function notation and use this to analyze and express features of functions represented in graphs and contextually. Students will use the tools of domain and range, rates of change, intercepts, and where a function is changing to describe contextual situations.
Unit 1 begins with a review of how to sketch a function from a contextual situation and then introduces function notation and features of functions, such as domain and range, intercepts, and rate of change. Students will learn that to describe the features of functions, they will need to identify the intervals over which the function is behaving in a certain manner. These intervals are described using inequalities in Algebra 1. As the unit progresses, students apply these features of functions to new parent functions—quadratic and exponential—as well as to systems previously learned in 8th grade, and model and analyze situations in these new parent functions. Students will be expected to translate features between the representations of graphs, tables, situations, and, in cases of some linear functions, equations.
As Algebra 1 progresses, students will apply this introduction to analyzing functions throughout the year, from Statistics to each of the functions studied more in-depth. Students will also expand their understanding of systems of functions beyond just linear systems to include thinking about systems of linear and quadratic equations, linear and exponential equations, etc. Skills learned in this unit will be revisited throughout Algebra 1, in Algebra 2, and in AP Calculus. This unit will provide students with a solid conceptual understanding of how functions can be used to model and interpret functions.
Pacing: 13 instructional days (11 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment:
Internalization of Trajectory of Unit:
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function | independent variable | dependent variable |
interval | function notation "f of x" | x-intercept/y-intercept |
system of functions | parent function | domain |
range | average rate of change/rate of change | quadratic functions |
parabola | exponential functions | solution |
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F.IF.B.4
F.IF.B.6
N.Q.A.1
N.Q.A.2
N.Q.A.3
Model a contextual linear situation graphically using appropriate scales and features.
F.IF.A.1
F.IF.A.2
Define functions and evaluate points in tables, graphs, and contextual situations using function notation.
F.IF.A.2
F.IF.C.9
Identify features of functions, including x-intercept and y-intercept, in context. Evaluate function notation in context.
F.IF.A.1
F.IF.C.9
Identify the domain and range through contextual situations, and explore domain and range on a graph. Represent domain and range with inequalities.
F.IF.A.2
F.IF.B.4
F.IF.B.6
Calculate and interpret the rate of change from two points on a graph, in a situation, or in function notation.
F.IF.B.4
Describe and sketch functions using the features of domain and range, intercepts, function behavior, and the value of the function.
F.IF.B.4
F.IF.B.5
F.IF.B.6
N.Q.A.2
Analyze the key features of a contextual situation and model these graphically.
F.IF.B.5
F.IF.C.7.A
A.CED.A.2
F.LE.A.3
Draw quadratic functions represented contextually. Identify key features of the graph and relate to context.
F.IF.B.5
F.IF.C.7.E
A.CED.A.2
F.LE.A.3
Sketch an exponential function that represents a situation. Identify key features of the graph and relate to context.
F.IF.A.2
F.IF.B.5
A.REI.D.11
Draw a graph to represent a system of functions. Identify the solution to a system represented graphically and in context.
F.IF.B.4
Analyze functions and identify parent functions of graphs. Identify variables of a situation and the scale of the associated graph. Represent a situation in a graph, table, and description.
Key: Major Cluster Supporting Cluster Additional Cluster
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