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# MAFS.912.F-LE.1.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Subject Area: Mathematics
Domain-Subdomain: Functions: Linear, Quadratic, & Exponential Models
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark will be assessed using: EE item(s)
• Also assesses:

MAFS.912.F-BF.1.1

MAFS.912.F-IF.1.3

• 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 input-output
pairs, at least two sets of pairs must have consecutive inputs.

In items that require the student to construct arithmetic or geometric
sequences, the real-world context should be discrete.

In items that require the student to construct a linear or exponential
function, the real-world 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 real-world context.

Students will write a linear function, an arithmetic sequence, an
exponential function, or a geometric sequence when given a verbal
description of a real-world 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 real-world 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 real-world 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 real-world 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 F-LE.1.2 and F-BF.1.1, items should be set in a real-world context.

For F-IF.1.3, items may be set in a mathematical or real-world
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 F-BF.1.1b and c, the student may be asked to find a value.

For F-LE.1.2 and F-BF.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.

### SAMPLE TEST ITEMS (1)

• 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