# MAFS.912.F-IF.1.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
General Information
Subject Area: Mathematics
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand the concept of a function and use function notation. (Algebra 1 - Major Cluster) (Algebra 2 - Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Also assesses:
MAFS.912.F-IF.1.1

MAFS.912.F-IF.2.5

• Assessment Limits :
For F-IF.1.2, in items that require the student to find a value given a
function, the following function types are allowed: quadratic,
polynomials whose degrees are no higher than 6, square root, cube
root, absolute value, exponential except for base e, and simple
rational.

Items may present relations in a variety of formats, including sets of
ordered pairs, mapping diagrams, graphs, and input/output models.

In items requiring the student to find the domain from graphs,
relationships may be on a closed or open interval.

In items requiring the student to find domain from graphs,
relationships may be discontinuous.

Items may not require the student to use or know interval notation.

• Calculator :

Neutral

• Clarification :
Students will evaluate functions that model a real-world context for
inputs in the domain.

Students will interpret the domain of a function within the real-world
context given.

Students will interpret statements that use function notation within
the real-world context given.

Students will use the definition of a function to determine if a
relationship is a function, given tables, graphs, mapping diagrams, or
sets of ordered pairs.

Students will determine the feasible domain of a function that models
a real-world context.

• Stimulus Attributes :
For F-IF.1.1, items may be set in a real-world or mathematical
context.

For F-IF.1.2, items that require the student to evaluate may be
written in a mathematical or real-world context. Items that require
the student to interpret must be set in a real-world context.

For F-IF.2.5, items must be set in a real-world context.
Items must use function notation

• Response Attributes :
For F-IF.2.5, items may require the student to apply the basic
modeling cycle.

Items may require the student to choose an appropriate level of
accuracy.

Items may require the student to choose and interpret the scale in a
graph.

Items may require the student to choose and interpret units.

Items may require the student to write domains using inequalities.

## Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912100: Fundamental Algebraic Skills (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.F-IF.1.AP.2a: Match the correct function notation to a function or a model of a function (e.g., x f(x) y).

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 3 - High School Algebra 1 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 1 - High School Algebra 1 State Interim Assessment:

This is the State Interim Assessment for high school.

Type: Assessment

## Formative Assessments

Cell Phone Battery Life:

Students are asked to interpret statements that use function notation in the context of a problem.

Type: Formative Assessment

What Is the Value?:

Students are asked to determine the corresponding input value for a given output using a table of values representing a function, f.

Type: Formative Assessment

What Is the Function Notation?:

Students are asked to use function notation to rewrite the formula for the volume of a cube and to explain the meaning of the notation.

Type: Formative Assessment

Graphs and Functions:

Students are asked to determine the value of a function, at an input given using function notation, by inspecting its graph.

Type: Formative Assessment

Evaluating a Function:

Students are asked to evaluate a function at a given value of the independent variable.

Type: Formative Assessment

## Lesson Plans

Representing Polynomials:

This lesson unit is intended to help you assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials as well as recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).

Type: Lesson Plan

Functions and Everyday Situations:

This lesson unit is intended to help you assess how well students are able to articulate verbally the relationships between variables arising in everyday contexts, translate between everyday situations and sketch graphs of relationships between variables, interpret algebraic functions in terms of the contexts in which they arise and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

Type: Lesson Plan

How much is your time worth?:

This lesson is designed to help students understand compound interest formulas as a function with respect to an independent variable. They will also be required to translate word problems into function models and use a graphing calculator to predict outcomes for various inputs.

Type: Lesson Plan

Freeze:

In this lesson students will learn how to write equations in function notation when given a real-world scenario. Students will work in groups to determine an equation for a given scenario, as well as, write a scenario for a given equation.

Type: Lesson Plan

Domain Representations:

This lesson asks students to use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions. The material allows students to examine and utilize connections between a function's symbolic representation, a function's graphical representation, and a function's domain.

Type: Lesson Plan

Exponential Graphing Using Technology:

This lesson is teacher/student directed for discovering and translating exponential functions using a graphing app. The lesson focuses on the translations from a parent graph and how changing the coefficient, base and exponent values relate to the transformation.

Type: Lesson Plan

## Original Student Tutorial

Travel with Functions:

Learn how to evaluate and interpret function notation by following Melissa and Jose on their travels in this interactive tutorial.

Type: Original Student Tutorial

Yam in the Oven:

The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example mistakenly interpreting f(x) as the product of f and x.

Using Function Notation II:

The purpose of the task is to explicitly identify a common error made by many students when using the "identity" f(x + h) = f(x) + f(h).

The Random Walk:

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation. The task could be used to segue the discussion from functions to probability, in particular the early standards in the S-CP domain.

Cell Phones:

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

The High School Gym:

This task asks students to consider functions in regard to temperatures in a high school gym.

Random Walk II:

These problems form a bridge between work on functions and work on probability. The task is better suited for instruction than for assessment as it provides students with a non-standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.

Pizza Place Promotion:

This tasks asks students to use functions to predict the price of a pizza on a specific day and find which day the pizza would be cheapest according to a promotion.

## Tutorial

Function Notation:

This tutorial will help the students to understand the function notation such as f(x), which can be thought as another way of representing the y-value in a function, especially when graphing. The y-axis is even labeled as the f(x) axis, when graphing.

Type: Tutorial

## Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

## MFAS Formative Assessments

Cell Phone Battery Life:

Students are asked to interpret statements that use function notation in the context of a problem.

Evaluating a Function:

Students are asked to evaluate a function at a given value of the independent variable.

Graphs and Functions:

Students are asked to determine the value of a function, at an input given using function notation, by inspecting its graph.

What Is the Function Notation?:

Students are asked to use function notation to rewrite the formula for the volume of a cube and to explain the meaning of the notation.

What Is the Value?:

Students are asked to determine the corresponding input value for a given output using a table of values representing a function, f.

## Original Student Tutorials Mathematics - Grades 9-12

Travel with Functions:

Learn how to evaluate and interpret function notation by following Melissa and Jose on their travels in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Travel with Functions:

Learn how to evaluate and interpret function notation by following Melissa and Jose on their travels in this interactive tutorial.

Type: Original Student Tutorial

Yam in the Oven:

The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example mistakenly interpreting f(x) as the product of f and x.

The Random Walk:

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation. The task could be used to segue the discussion from functions to probability, in particular the early standards in the S-CP domain.

Cell Phones:

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

The High School Gym:

This task asks students to consider functions in regard to temperatures in a high school gym.

Random Walk II:

These problems form a bridge between work on functions and work on probability. The task is better suited for instruction than for assessment as it provides students with a non-standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.

Pizza Place Promotion:

This tasks asks students to use functions to predict the price of a pizza on a specific day and find which day the pizza would be cheapest according to a promotion.

## Tutorial

Function Notation:

This tutorial will help the students to understand the function notation such as f(x), which can be thought as another way of representing the y-value in a function, especially when graphing. The y-axis is even labeled as the f(x) axis, when graphing.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Yam in the Oven:

The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example mistakenly interpreting f(x) as the product of f and x.

The Random Walk:

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation. The task could be used to segue the discussion from functions to probability, in particular the early standards in the S-CP domain.

Cell Phones:

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

The High School Gym:

This task asks students to consider functions in regard to temperatures in a high school gym.