Secondary Mathematics I

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.1-3). Interpret linear or exponential functions that arise in applications in terms of a context (Standards F.IF.4-6). Analyze linear or exponential functions using different representations (Standards F.IF.7, 9).

Standard F.IF.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, compare the growth of two linear functions, or two exponential functions such as y=3n and y=100•2n.

• 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.
• 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.
• Graphs of Power Functions
This task requires students to recognize the graphs of different (positive) powers of x.
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.
• 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 8: Connecting Algebra & Geometry - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 8, Connecting Algebra and Geometry, students use the Pythagorean Theorem to find the distance between two points and to derive the distance formula.
• Module 8: Connecting Algebra & Geometry - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 8 Teacher Notes, Connecting Algebra and Geometry, students use the Pythagorean Theorem to find the distance between two points and to derive the distance formula.
• 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.
• Representing Functions and Relations
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.
• Representing Functions and Relations video
Explains how algebra can be used to describe, represent and predict relations.
• 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.