Unit 5

Functions

Unit Narrative

In this unit, students expand and deepen their understanding of functions. They begin with a reminder of the definition of a function (a rule that assigns exactly one output to each input) that they previously saw in grade 8, then get familiar with function notation and use it to compare and analyze functions, write rules for functions, and solve for inputs or outputs.

Then, students explore graphs of functions to describe features such as “maximum,” “minimum,” “intercepts,” “increasing,” “decreasing,” and “average rate of change” and make connections between the graphs...

to access Pre-Unit Assessments.

Section A

Section Goals

Section Narrative

In this section, students recall the definition of a function as a rule that assigns no more than one output to every input. Then, they use function notation, like or , to describe rules from real-world situations and understand how the notation differentiates between input and output values.

<p>Two functions. months after free trial and cost (dollars).</p>

Let’s look at some fun functions around us and try to describe them!

Let’s learn about a handy way to refer to and talk about a function.

Let’s use function notation to talk about functions.

Let’s look at some rules that describe functions and write some too.

Let’s graph and find the values of some functions.

to access Section Checkpoints.

Section A

Let’s look at some fun functions around us and try to describe them!

Let’s learn about a handy way to refer to and talk about a function.

Let’s use function notation to talk about functions.

Let’s look at some rules that describe functions and write some too.

Let’s graph and find the values of some functions.

Section B

Section Goals

Section Narrative

In this section, students analyze graphs of functions including special features, such as “maximum,” “minimum,” “intercepts,” and “average rate of change.” They make connections between descriptions of real-life situations and graphs of functions that model those situations. Then they compare situations using graphs and function notation.

<p>Graph. Horizontal axis, 9 o’clock to 8 o’clock, time. Vertical axis, 25 to 50 by 5’s, temperature in degrees Fahrenheit. Graph is linear piecewise. Starts at 0 comma 35.</p>

Let’s use graphs of functions to learn about situations.

Let’s measure how quickly the output of a function changes.

Let’s sketch graphs to represent situations.

Let’s compare graphs of functions to learn about the situations they represent.

to access Section Checkpoints.

to access Mid-Unit Assessments.

Section B

Let’s use graphs of functions to learn about situations.

Let’s measure how quickly the output of a function changes.

Let’s sketch graphs to represent situations.

Let’s compare graphs of functions to learn about the situations they represent.

Section C

Section Goals

Section Narrative

In this section, students focus on the domain and range of various functions. The language of domain and range allows students to better understand piecewise functions for which different rules apply to different parts of the domain. In particular, students explore absolute value functions by way of a situation in which students determine how far away guesses are from an...

Let’s find all possible inputs and outputs for a function.

Let’s analyze graphs of functions to learn about their domain and range.

Let’s look at functions that are defined in pieces.

Let’s make some guesses and see how good they are.

Let’s investigate distance as a function.

to access Section Checkpoints.

Section C

Let’s find all possible inputs and outputs for a function.

Let’s analyze graphs of functions to learn about their domain and range.

Let’s look at functions that are defined in pieces.

Let’s make some guesses and see how good they are.

Let’s investigate distance as a function.

Section D

Section Goals

Section Narrative

In this section, students work with inverse functions as a way to find input values that correspond to known output values. Initially, students use the idea of writing a secret code to motivate the need to find the input that produced a given output. Then, they are provided contexts in which it is efficient to use the inverse to find...

Let’s define functions forward and backward.

Let’s find the inverses of linear functions.

Let’s use inverse functions to solve problems.

to access Section Checkpoints.

Section D

Let’s define functions forward and backward.

Let’s find the inverses of linear functions.

Let’s use inverse functions to solve problems.

Section E

Section Narrative

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

Let’s use functions to model data and make predictions.

to access Section Checkpoints.

Section E

Let’s use functions to model data and make predictions.

to access End-of-Unit Assessments.

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Functions

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