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Mathematics - Secondary Curriculum Secondary Mathematics I
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Strand: FUNCTIONS - Interpreting Linear and Exponential Functions (F.IF)

Understand the concept of a linear or exponential function and use function notation. Recognize arithmetic and geometric sequences as examples of linear and exponential functions (Standards F.IF.13). Interpret linear or exponential functions that arise in applications in terms of a context (Standards F.IF.46). Analyze linear or exponential functions using different representations (Standards F.IF.7, 9).

Standard F.IF.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • Analyzing Graphs
    This task could be used as a review problem or as an assessment problem after many different types of functions have been discussed. Since the different parameters of the functions are not given explicitly, the focus is not just on graphing specific functions but rather students have to focus on how values of parameters are reflected in a graph.
  • Bank Account Balance
    The purpose of this task is to study an example of a function which varies discretely over time.
  • Derivate
    Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
  • Exponential Kiss
    The purpose of this task is twofold: first using technology to study the behavior of some exponential and logarithmic graphs and secondly to manipulate some explicit logarithmic and exponential expressions.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • FUNCTIONS - Interpreting Linear and Exponential Functions (F.IF) - Sec Math I Core Guide
    The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics I Interpreting Linear and Exponential Functions (F.IF).
  • Graphing Calculator
    A free online graphing calculator.
  • Graphing Rational Functions
    This task starts with an exploration of the graphs of two functions whose expressions look very similar but whose graphs behave completely differently.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • Graphs of Power Functions
    This task requires students to recognize the graphs of different (positive) powers of x.
  • Graphs of Quadratic Functions
    This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is. It is effective after students have graphed parabolas in vertex form, but have not yet explored graphing other forms.
  • Identifying Exponential Functions
    The task is an introduction to the graphing of exponential functions.
  • Identifying graphs of functions
    The goal of this task is to get students to focus on the shape of the graph of an equation and how this changes depending on the sign of the exponent and on whether the exponential is in the numerator or denominator.
  • Introduction to the Materials (Math 1)
    Introduction to the Materials in the Mathematics One of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
  • Linear Functions
    The applet in this lesson allows students to manipulate variables and see the changes in the graphed line.
  • Modeling London's Population
    The purpose of this task is to model the population data for London with a variety of different functions. In addition to the linear, quadratic, and exponential models, this task introduces an additional model, namely the logistic model.
  • Module 2: Linear & Exponential Functions - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 2, Linear and Exponential Functions, begins with a learning cycle that introduces contexts with continuous domains and defining linear functions as having a constant rate of change and exponential functions as having a constant ratio over equal intervals.
  • Module 2: Linear & Exponential Functions - Teacher Notes (Math 1)
    Mathematics Vision Project, Secondary Math One Module 2 Teacher Notes, Linear and Exponential Functions, begins with a learning cycle that introduces contexts with continuous domains and defining linear functions as having a constant rate of change and exponential functions as having a constant ratio over equal intervals.
  • Module 3: Features of Functions - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 3, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
  • Module 3: Features of Functions - Teacher Notes (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 3 Teacher Notes, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
  • More Complicated Functions: Introduction to Linear Functions
    This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
  • Multi-Function Data Flyer
    The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
  • Proportional Functions
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Reading Graphs
    Through this lesson students will understand how to graph functions.
  • Representing Polynomials
    This lesson unit is intended to help educators assess how well students are able to translate between graphs and algebraic representations of polynomials.
  • Running Time
    This task provides an application of polynomials in computing. This purpose of this task is to serve as an introduction, and motivation, for the study of end behavior of polynomials, content specifically addresses in standard F-IF.C7c.
  • Student Task: Sorting Functions
    Students are given four graphs, four equations, four tables, and four rules. Their task is to match each graph with an equation, a table and a rule.


UEN logo http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.