**Subject Area:**Mathematics

**Grade:**912

**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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Exponential functions represented in graphs or tables should be able to be written in the form a + k.For exponential relationships, tables or graphs must contain at least one pair of consecutive values.

**Calculator :**Neutral

**Clarification :**

Students will compare a linear function and an exponential function

given in real-world context by interpreting the functions’ graphs.Students will compare a linear function and an exponential function

given in a real-world context through tables.Students will compare a quadratic function and an exponential

function given in real-world context by interpreting the functions’

graphs.Students will compare a quadratic function and an exponential

function given in a real-world context through tables**Stimulus Attributes :**

Items should give a graph or a table.Items should be given in a real-world context.

Items must use function notation

**Response Attributes :**

Items may require the student to apply the basic modeling cycle.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

**Test Item #:**Sample Item 1**Question:**The function f(x) models the value of goods that are imported into the United States, where x is the number of years since 1990. The function g(x) models the value of goods that are exported from the United States.

If f(x) and g(x) continue to model the importing and exporting of goods, then sometime in 2041, which is 51 years after 1990, f(x)=g(x).

Determine which function is exponential. Use the table of values to justify your answer.

Type your answer in the space provided. Be sure to include your function choice.

**Difficulty:**N/A**Type:**OR: Open Response

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Unit/Lesson Sequence

## Virtual Manipulatives

## MFAS Formative Assessments

Students are asked to compare a linear function and an exponential function in context.

Students are asked to compare a quadratic and an exponential function in context.

## Student Resources

## Problem-Solving Tasks

In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).

Type: Problem-Solving Task

The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Students' intuitions will probably have them favoring Option A for much longer than is actually the case, especially if they are new to the phenomenon of exponential growth. Teachers might use this surprise as leverage to segue into a more involved task comparing linear and exponential growth.

Type: Problem-Solving Task

This problem solving task shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

This task asks students to calculate exponential functions with a base larger than one.

Type: Problem-Solving Task

## Virtual Manipulatives

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

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

## Problem-Solving Tasks

In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).

Type: Problem-Solving Task

The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Students' intuitions will probably have them favoring Option A for much longer than is actually the case, especially if they are new to the phenomenon of exponential growth. Teachers might use this surprise as leverage to segue into a more involved task comparing linear and exponential growth.

Type: Problem-Solving Task

This problem solving task shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

This task asks students to calculate exponential functions with a base larger than one.

Type: Problem-Solving Task