(F) Functions Categories All categories Not categorized Prioritized Standards (EE) Expressions and Equations (F) Functions (G) Geometry (NS) The Number System (SP) Statistics and Probability

# Functions

• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.

## Domain Description

Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.

## Standards in this Domain

• MAT-08.F.01 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required for Grade 8)
• MAT-08.F.02 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
• MAT-08.F.03 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
• MAT-08.F.04 - Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
• MAT-08.F.05 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.F.01

 8th Grade MAT Targeted StandardsDomain (F) FunctionsCluster: Define, evaluate, and compare functions. MAT-08.F.01 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

## Student Learning Targets:

### Knowledge Targets

• I can understand that in a function, each input has only one output.

### Reasoning Targets

• I can evaluate a function.
• I can complete an input-output table accurately.
• I can describe the domain and the range of a function.
• I can determine whether a given graph or table represents a function.

### Skills Domain (Performance) Targets

• I can graph a function from a table.

## Resources

### Vocabulary

• function
• domain
• range
• input
• output
• discrete
• continuous
• linear
• nonlinear

#### MAT-08.F.02

 8th Grade MAT Targeted StandardsDomain (F) FunctionsCluster: Define, evaluate, and compare functions MAT-08.F.02 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

## Student Learning Targets:

### Reasoning Targets

• I can determine the properties of a function written in algebraic form (slope, y-intercept, linear, nonlinear).
• I can determine the properties of a function given the inputs and outputs in a table.
• I can determine the properties of a function represented as a graph.
• I can determine the properties of a function given verbally.

### Skills Domain (Performance) Targets

I can compare properties of two functions each represented in a different way.

## Resources

### Vocabulary

• rate of change

#### MAT-08.F.03

Domain (F) Functions
Cluster: Define, evaluate, and compare functions

MAT-08.F.03 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-11-12.5.2 Generate graphs of a variety of functions (i.e., linear, quadratic, polynomial, absolute value, and exponential), using technology when appropriate.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.F.04

Domain (F) Functions
Cluster: Define, evaluate, and compare functions

MAT-08.F.04 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y)values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.F.05

Domain (F) Functions
Cluster: Define, evaluate, and compare functions.

MAT-08.F.05 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-11-12.5.2 Generate graphs of a variety of functions (i.e., linear, quadratic, polynomial, absolute value, and exponential), using technology when appropriate.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards