Curriculum / Math / 9th Grade / Unit 1: Functions, Graphs and Features / Lesson 2
Math
Unit 1
9th Grade
Lesson 2 of 11
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Define functions and evaluate points in tables, graphs, and contextual situations using function notation.
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.
The foundational standards covered in this lesson
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Below is an example of a relation that is a function and an example of a relation that is not a function.
What are the defining characteristics of a function?
FUNCTION:
NOT A FUNCTION:
Use the graph below to answer the questions that follow:
Function notation describes a particular relationship and implies the dependency of variables.
The general form of function notation is $${f(x) = y}$$. $$y$$ is dependent on $${x }$$.
Part A: The function $$f$$ above has a point $$f(-2) = 1$$. Mark this point on the graph above.
Part B: Find the $$x$$ or $$y$$ values from the graph noted by the function notation below.
$$f(-9)=$$
$$f(x)=1$$
$$f(x)=-2$$
$$f(4)=$$
$$g(x)=5$$
$${g(0)=}$$
John was running a race, and his coach was timing him. John’s race can be described as the distance in meters, $$d$$, as a function of time in seconds, $$t$$. Partway through the race, John’s position could be described as $$d(6)=50$$. Describe John’s time and distance at this point.
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
Suppose $$f$$ is a function.
Points on a Graph, accessed on June 22, 2017, 3:51 p.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.
Let $${f(t)}$$ be the number of people, in millions, who own cell phones $$t$$ years after 1990. Explain the meaning of the following statements.
Cell Phones, accessed on June 22, 2017, 3:53 p.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.
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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Identify features of functions, including x-intercept and y-intercept, in context. Evaluate function notation in context.
Topic A: Features of Functions
Model a contextual situation graphically using appropriate scales and features.
Standards
F.IF.B.4F.IF.B.6N.Q.A.1N.Q.A.2N.Q.A.3
F.IF.A.1F.IF.A.2
F.IF.A.2F.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.1F.IF.B.5
Calculate and interpret the rate of change from two points on a graph, in a situation, or in function notation.
F.IF.A.2F.IF.B.4F.IF.B.6
Describe and sketch functions using the features of domain and range, intercepts, function behavior, and the value of the function.
F.IF.B.4
Analyze the key features of a contextual situation and model these graphically.
F.IF.B.4F.IF.B.5F.IF.B.6N.Q.A.2
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Topic B: Nonlinear Functions
Draw quadratic functions represented contextually. Identify key features of the graph and relate to context.
A.CED.A.2F.IF.B.5F.IF.C.7.AF.LE.A.3
Sketch an exponential function that represents a situation. Identify key features of the graph and relate to context.
A.CED.A.2F.IF.B.5F.IF.C.7.EF.LE.A.3
Draw a graph to represent a system of functions. Identify the solution to a system represented graphically and in context.
A.REI.D.11F.IF.A.2F.IF.B.5
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.
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