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Mathematics - Secondary Curriculum Secondary Mathematics I
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Strand: FUNCTIONS - Building Linear or Exponential Functions (F.BF)

Build a linear or exponential function that models a relationship between two quantities (Standards F.BF.12). Build new functions from existing functions (Standard F.BF.3).

Standard F.BF.3

Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y-intercept. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

  • ALGEBRA - Seeing Structure in Expressions (A.SSE) - 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 - Seeing Structure in Expressions (A.SSE)
  • Building a General Quadratic Function
    This task is for instructional purposes only and builds on ''Building an explicit quadratic function.'' First, it is vital that students have worked through ''Building an explicit quadratic function'' before undertaking this task.
  • Building a quadratic function from f(x)=x2
    This is the first of a series of tasks aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function. Here the student works with an explicit function and studies the impact of scaling and linear change of variables.
  • Building an Explicit Quadratic Function by Composition
    This task is intended for instruction and to motivate the task Building a General Quadratic Function. This task assumes that the students are familiar with the process of completing the square.
  • Exploring Sinusoidal Functions
    This task serves as an introduction to the family of sinusoidal functions. It uses a desmos applet to let students explore the effect of changing the parameters in y=Asin(B(x−h))+k on the graph of the function.
  • 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 - Building Linear or Exponential Functions (F.BF) - 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 - Building Linear or Exponential Functions (F.BF)
  • Generalizing Patterns: Table Tiles
    This lesson unit is intended to help educators assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • Identifying Even and Odd Functions
    This task includes an experimental GeoGebra worksheet, with the intent that instructors might use it to more interactively demonstrate the relevant content material.
  • Identifying Quadratic Functions (Vertex Form)
    This task has students explore the relationship between the three parameters a, h, and k in the equation f(x)=a(xh)2+k and the resulting graph.
  • 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.
  • Medieval Archer
    This task addresses the first part of standard F-BF.3: “Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).” Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.
  • 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.
  • 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.
  • Sample Assessment Task: Quadratic transformation
    This is a two-part assessment task. Part A asks students to interpret the symbolic representation of a transformation on a function. Part B is about connecting the representations of a function. Use the navigation at the upper right of this page to access the task.
  • Tidal Waves (pdf)
    Students analyze a problem faced by the captain of a shipping vessel. Students may use a range of functions to model the situation and reflect on their usefulness. Because trigonometric functions can be useful, this task would be particularly appropriate for students who have had an introduction to graphing sine and cosine functions.
  • Transforming the graph of a function
    Like "Building functions: concrete case'' this task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.


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.