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Functions

8th Grade

Alabama Course of Study Standards: 13

Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.

Arkansas Academic Standards: 8.F.A.1

  • 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
Note: An informal discussion of function notation is needed; however, student assessment is not required.

Arizona - K-12 Academic Standards: 8.F.A.1

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 in Grade 8.)

Common Core State Standards: Math.8.F.1 or 8.F.A.1

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.

Georgia Standards of Excellence (GSE): 8.FGR.5.1

Show and explain that a function is a rule that assigns to each input exactly one output.

Louisiana Academic Standards: 8.F.A.1

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 in this grade level.)

North Carolina - Standard Course of Study: 8.F.1

Understand that a function is a rule that assigns to each input exactly one output.
  • Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output.
  • Recognize functions given a table of values or a set of ordered pairs.

New York State Next Generation Learning Standards: 8.F.1

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.
Note: The terms domain and range may be introduced at this level; however, these terms are formally introduced in Algebra I (AI-F.IF.1).

Ohio's Learning Standards: 8.F.1

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 in Grade 8.

Tennessee Academic Standards: 8.F.A.1

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 in 8th grade.)

Wisconsin Academic Standards: 8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a numerically valued function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.

Alabama Course of Study Standards: 15

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
  1. Distinguish between linear and non-linear functions.

Arkansas Academic Standards: 8.F.A.2

Compare properties (e.g., y-intercept/initial value, slope/rate of change) of two functions each represented in a different way (e.g., algebraically, graphically, numerically in tables, or by verbal descriptions)

Common Core State Standards: Math.8.F.2 or 8.F.A.2

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.

Georgia Standards of Excellence (GSE): 8.FGR.5.4

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

North Carolina - Standard Course of Study: 8.F.2

Compare properties of two linear functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

New York State Next Generation Learning Standards: 8.F.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
e.g., Given a linear function represented by a table of values and a linear function represented by an algebraic equation, determine which function has the greater rate of change.

Wisconsin Academic Standards: 8.F.A.2

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.

Alabama Course of Study Standards: 14

Evaluate functions defined by a rule or an equation, given values for the independent variable.

Arkansas Academic Standards: 8.F.A.3

Identify the unique characteristics of functions (e.g., linear, quadratic, and exponential) by comparing their graphs, equations, and input/output tables

Arizona - K-12 Academic Standards: 8.F.A.3

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 in not linear because its graph contains the points (1,1), (2,4), and (3,9) which are not on a straight line.

Common Core State Standards: Math.8.F.3 or 8.F.A.3

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.

Georgia Standards of Excellence (GSE): 8.FGR.5.5

Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x-x1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.

North Carolina - Standard Course of Study: 8.F.3

Identify linear functions from tables, equations, and graphs.

New York State Next Generation Learning Standards: 8.F.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.
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.

Wisconsin Academic Standards: 8.F.A.3

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.

Alabama Course of Study Standards: 17

Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Arkansas Academic Standards: 8.F.B.5

  • Describe 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 features of a function that has been described verbally

Common Core State Standards: Math.8.F.5 or 8.F.B.5

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.

Georgia Standards of Excellence (GSE): 8.FGR.5.9

Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.

North Carolina - Standard Course of Study: 8.F.5

Qualitatively analyze the functional relationship between two quantities.
  • Analyze a graph determining where the function is increasing or decreasing; linear or non-linear.
  • Sketch a graph that exhibits the qualitative features of a real-world function.

New York State Next Generation Learning Standards: 8.F.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph.
e.g., where the function is increasing or decreasing or when the function is linear or non-linear
Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context.

Pennsylvania Core Standards: CC.2.2.8.C.1

Define, evaluate, and compare functions.

Pennsylvania Core Standards: M08.B-F.1.1.1

Determine whether a relation is a function.

Pennsylvania Core Standards: M08.B-F.1.1.2

Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions).

Pennsylvania Core Standards: M08.B-F.1.1.3

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.

Pennsylvania Core Standards: M08.B-F.2.1.2

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 or determine a graph that exhibits the qualitative features of a function that has been described verbally.

Florida - Benchmarks for Excellent Student Thinking: MA.8.F.1.1

Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.

Florida - Benchmarks for Excellent Student Thinking: MA.8.F.1.2

Given a function defined by a graph or an equation, determine whether the function is a linear function.Given an input-output table, determine whether it could represent a linear function.

Florida - Benchmarks for Excellent Student Thinking: MA.8.F.1.3

Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant.

8th Grade Math - Functions Lesson
 



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