 Graph linear and quadratic functions and show intercepts, maxima, and minima.
 Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.
 Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.
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.

Assessed with:
MAFS.912.FIF.3.8
Related Courses
Related Access Points
Related Resources
Educational Software / Tool
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Experts
Perspectives Video: Professional/Enthusiast
ProblemSolving Tasks
Tutorials
Unit/Lesson Sequences
Video/Audio/Animation
Virtual Manipulatives
Worksheet
MFAS Formative Assessments
Students are asked to graph a linear function and to find the intercepts of the function as well as the maximum and minimum of the function within a given interval of the domain.
Students are asked to graph a quadratic function and answer questions about the intercepts, maximum, and minimum.
Students are asked to graph a rational function with the use of technology and identify key features of the graph.
Students are asked to graph a step function, state the domain of the function, and name any intercepts.
Students are asked to graph an exponential function and to determine if the function is an example of exponential growth or decay, describe any intercepts, and describe the end behavior of the graph.
Students are asked to graph two root functions and answer questions about the domain, maxima, and minima.
Original Student Tutorials Mathematics  Grades 912
Follow as we discover key features of a quadratic equation written in vertex form in this interactive tutorial.
Student Resources
Original Student Tutorial
Follow as we discover key features of a quadratic equation written in vertex form in this interactive tutorial.
Type: Original Student Tutorial
Perspectives Video: Experts
<p>Jump to it and learn more about how quadratic equations are used in robot navigation problem solving!</p>
Type: Perspectives Video: Expert
The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?
Download the CPALMS Perspectives video student note taking guide.
Type: Perspectives Video: Expert
ProblemSolving Tasks
This problemsolving task challenges students to find all quadratic functions described by given equation and coordinates, and describe how the graphs of those functions are related to one another.
Type: ProblemSolving Task
Students compare graphs of different quadratic functions, then produce equations of their own to satisfy given conditions.
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 (y=a(x–h)^{2}+k), but have not yet explored graphing other forms.
Type: ProblemSolving Task
This task requires students to recognize the graphs of different (positive) powers of x.
Type: ProblemSolving Task
Tutorials
You will learn how the parent function for a quadratic function is affected when f(x) = x^{2}.
Type: Tutorial
This tutorial will help the students to identify the vertex of a parabola from the equation, and then graph the parabola.
Type: Tutorial
This tutorial helps the learners to graph the equation of a quadratic function using the coordinates of the vertex of a parabola and its x intercepts.
Type: Tutorial
This tutorial will help you to learn about exponential functions by graphing various equations representing exponential growth and decay.
Type: Tutorial
Video/Audio/Animation
Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1"
Type: Video/Audio/Animation
Virtual Manipulatives
In this activity, students adjust slider bars which adjust the coefficients and constants of a linear function and examine how their changes affect the graph. The equation of the line can be in slopeintercept form or standard form. This activity allows students to explore linear equations, slopes, and yintercepts and their visual representation on a graph. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
This resource provides linear functions in standard form and asks the user to graph it using intercepts on an interactive graph below the problem. Immediate feedback is provided, and for incorrect responses, each step of the solution is thoroughly modeled.
Type: Virtual Manipulative
Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.
Type: Virtual Manipulative
Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
With a mouse, students will drag data points (with their error bars) and watch the bestfit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.
Type: Virtual Manipulative
This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).
Type: Virtual Manipulative
Parent Resources
ProblemSolving Tasks
This problemsolving task challenges students to find all quadratic functions described by given equation and coordinates, and describe how the graphs of those functions are related to one another.
Type: ProblemSolving Task
Students compare graphs of different quadratic functions, then produce equations of their own to satisfy given conditions.
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 (y=a(x–h)^{2}+k), but have not yet explored graphing other forms.
Type: ProblemSolving Task
This task requires students to recognize the graphs of different (positive) powers of x.
Type: ProblemSolving Task
Video/Audio/Animation
Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1"
Type: Video/Audio/Animation
Virtual Manipulative
Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.
Type: Virtual Manipulative