Curriculum / Math / 9th Grade / Unit 5: Functions and Transformations / Lesson 3
Math
Unit 5
9th Grade
Lesson 3 of 16
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Evaluate a piecewise function written algebraically, with and without context.
The core standards covered in this lesson
F.IF.A.1 — Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. 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. The graph of f is the graph of the equation y = f(x).
F.IF.A.2 — Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
A.SSE.A.1.A — Interpret parts of an expression, such as terms, factors, and coefficients.
The foundational standards covered in this lesson
8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A piecewise graph is defined below.
Evaluate the values below.
In order to gain popularity among students, a new pizza place near school plans to offer a special promotion. The cost of a large pizza (in dollars) at the pizza place as a function of time (measured in days since February 10th) may be described as
(Assume $$t$$ only takes whole number values.)
Pizza Place Promotion, accessed on May 10, 2018, 10:46 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A museum offers discounted rates for large groups following the rules below.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Write and graph piecewise functions from contextual situations.
Topic A: Piecewise Functions
Write equations and graph linear relationships with different domains.
Standards
A.CED.A.1A.CED.A.2A.CED.A.3F.IF.B.5F.IF.C.7
Graph piecewise functions presented algebraically and write piecewise functions from graphs.
F.IF.A.2F.IF.B.4F.IF.C.7.B
A.SSE.A.1.AF.IF.A.1F.IF.A.2
A.CED.A.2A.CED.A.3F.IF.B.5
Graph, evaluate, and write step functions, with and without context.
A.CED.A.3F.IF.A.1F.IF.C.7.B
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Topic B: Absolute Value Functions
Graph absolute value functions in the coordinate plane and identify domain and range.
F.BF.B.3F.IF.B.4F.IF.B.5F.IF.C.7.BF.IF.C.9
Identify the solutions to an absolute value equation.
A.REI.A.1A.REI.D.11
Solve absolute value equations algebraically and identify extraneous solutions.
A.REI.B.3
Identify the solution(s) to an absolute value inequality.
A.REI.A.1A.REI.B.3A.REI.D.11F.IF.B.4F.IF.C.7.B
Solve absolute value inequalities algebraically and verify graphically.
Identify solutions to a system of absolute value and linear functions graphically and algebraically.
A.REI.A.1A.REI.C.6A.REI.D.11
Topic C: Function Transformations
Identify and describe vertical translations of functions.
F.BF.B.3F.IF.B.4F.IF.B.5
Identify and describe horizontal translations of functions.
F.BF.B.3F.IF.B.5
Identify and describe vertical scaling of functions, including reflections over the $$x$$-axis.
Identify and describe horizontal scaling of functions, including reflections over the $$y$$-axis.
Apply transformations to functions.
F.BF.B.3
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