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.

Also assesses:
 Assessment Limits :
In items where the student must write a function using arithmetic
operations or by composing functions, the student should have to
generate the new function only.In items where the student constructs an exponential function, a
geometric sequence, or a recursive definition from inputoutput
pairs, at least two sets of pairs must have consecutive inputs.In items that require the student to construct arithmetic or geometric
sequences, the realworld context should be discrete.In items that require the student to construct a linear or exponential
function, the realworld context should be continuous.  Calculator :
Neutral
 Clarification :
Students will write a linear function, an arithmetic sequence, an
exponential function, or a geometric sequence when given a graph
that models a realworld context.Students will write a linear function, an arithmetic sequence, an
exponential function, or a geometric sequence when given a verbal
description of a realworld context.Students will write a linear function, an arithmetic sequence, an
exponential function, or a geometric sequence when given a table of
values or a set of ordered pairs that model a realworld context.Students will write an explicit function, define a recursive process, or
complete a table of calculations that can be used to mathematically
define a realworld context.Students will write a function that combines functions using
arithmetic operations and relate the result to the context of the
problem.Students will write a function to model a realworld context by
composing functions and the information within the context.Students will write a recursive definition for a sequence that is
presented as a sequence, a graph, or a table.  Stimulus Attributes :
For FLE.1.2 and FBF.1.1, items should be set in a realworld context.For FIF.1.3, items may be set in a mathematical or realworld
context.Items must use function notation.
In items where the student builds a function using arithmetic
operations or by composition, the functions may be given using
verbal descriptions, function notation or as equations.  Response Attributes :
For FBF.1.1b and c, the student may be asked to find a value.For FLE.1.2 and FBF.1.1, items may require the student to apply the
basic modeling cycle.In items where the student writes a recursive formula, the student
may be expected to give both parts of the formula.The student may be required to determine equivalent recursive
formulas or functions.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.
MAFS.912.FBF.1.1
MAFS.912.FIF.1.3
 Test Item #: Sample Item 1
 Question:
A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the university in 2015 was $33,741.
The function, B(x), models the estimated tuition cost, where x is the number of years since 2015.
Click on the blank to enter an expression that completes the function B(x).
 Difficulty: N/A
 Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
ProblemSolving Tasks
Unit/Lesson Sequences
Virtual Manipulatives
MFAS Formative Assessments
Students are asked to write a function to model the relationship between two variables described in a realworld context.
Students are asked to write function rules for sequences given tables of values.
Students are given a table of values and are asked to write a linear function.
Students are asked to write an exponential function from a written description of an exponential relationship.
Students are asked to write an exponential function represented by a table of values.
Students are asked to write an exponential function given its graph.
Original Student Tutorials Mathematics  Grades 912
Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.
Student Resources
Original Student Tutorial
Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.
Type: Original Student Tutorial
ProblemSolving Tasks
In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.
Type: ProblemSolving Task
This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.
Type: ProblemSolving Task
This problem solving tasks asks students to find the values of points on a graph.
Type: ProblemSolving Task
This problem solving task asks students to graph a function and find the values of points on a graph.
Type: ProblemSolving Task
The task provides an opportunity for students to engage in detailed analysis of the rate of change of the elevation.
Type: ProblemSolving Task
This problem is an exponential function example that uses the realworld problem of how fast rumors spread.
Type: ProblemSolving Task
This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2.
Type: ProblemSolving Task
This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2. First, the ycoordinates of R1 and R2 cannot have different signs, that is it cannot be that one is positive while the other is negative. This is because the function g(x) = ex takes only positive values. Consequently, f(x) = ae^bx cannot take both positive and negative values. Furthermore, the only way aebx can be zero is if a = 0 and then the function is linear rather than exponential. As long as the ycoordinates of R1 and R2 are nonzero and have the same sign, there is a unique exponential function f(x) = ae^bx whose graph contains R1 and R2.
Type: ProblemSolving Task
This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies.
Type: ProblemSolving Task
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
Type: ProblemSolving Task
In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (FLE.2, FLE.3, AREI.11).
Type: ProblemSolving Task
This task asks students to write equations to predict how much money will be in a savings account at the end of each year, based on different factors like interest rates.
Type: ProblemSolving Task
Virtual Manipulatives
In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(yintercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. 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
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
Parent Resources
ProblemSolving Tasks
In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.
Type: ProblemSolving Task
This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.
Type: ProblemSolving Task
This problem solving tasks asks students to find the values of points on a graph.
Type: ProblemSolving Task
This problem solving task asks students to graph a function and find the values of points on a graph.
Type: ProblemSolving Task
The task provides an opportunity for students to engage in detailed analysis of the rate of change of the elevation.
Type: ProblemSolving Task
This problem is an exponential function example that uses the realworld problem of how fast rumors spread.
Type: ProblemSolving Task
This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2.
Type: ProblemSolving Task
This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2. First, the ycoordinates of R1 and R2 cannot have different signs, that is it cannot be that one is positive while the other is negative. This is because the function g(x) = ex takes only positive values. Consequently, f(x) = ae^bx cannot take both positive and negative values. Furthermore, the only way aebx can be zero is if a = 0 and then the function is linear rather than exponential. As long as the ycoordinates of R1 and R2 are nonzero and have the same sign, there is a unique exponential function f(x) = ae^bx whose graph contains R1 and R2.
Type: ProblemSolving Task
This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies.
Type: ProblemSolving Task
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
Type: ProblemSolving Task
In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (FLE.2, FLE.3, AREI.11).
Type: ProblemSolving Task
This task asks students to write equations to predict how much money will be in a savings account at the end of each year, based on different factors like interest rates.
Type: ProblemSolving Task