8.FGR.5Functions & Graphical Models

Expectations

• 8.FGR.5.1

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

• 8.FGR.5.2

  Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

• 8.FGR.5.3

  Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.

• 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).

• 8.FGR.5.5

  Write and explain the equations $y = mx + b$ (slope-intercept form), $Ax + By = C$ (standard form), and $(y - y_1) = m(x - x_1)$ (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.

• 8.FGR.5.6

  Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

• 8.FGR.5.7

  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.

• 8.FGR.5.8

  Explain the meaning of 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.

• 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.

Georgia Milestones coverage

• Mathematics Grade 8 (EOG) · Functional & Graphical Reasoning

  Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.

  about 17% of the test · 10 points

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Know the meaning of the domain of a function. Determine the initial value and rate of change of a function. Identify an equation written in one of the three forms as a linear function. Determine the rate of change when given a relationship.

Developing

Recognize whether a relationship is a function. Identify and describe functions based on qualitative features (e.g., linear or nonlinear, increasing or decreasing). Identify the domain of a function when given a table or graphic representation. Compare the initial values and rates of change of two functions represented in the same way. Given specific information, write a linear equation in any form. Determine the initial value when given a table or graph. Given a linear equation in any form, graph the function on a coordinate grid.

Proficient

Explain how a function rule assigns each input to exactly one output. Create and interpret graphs of linear and nonlinear functions that exhibit qualitative features based on realistic situations. Relate the domain of a function to the given real-world or mathematical context. Compare the initial values and rates of change of two functions represented in different ways. Rewrite linear equations in a different form. Explain when to use each form of an equation. Construct linear functions to model relationships in realistic mathematical problems or from a pair of (x, y) values. Explain the meaning of the rate of change and initial value of a linear function in terms of the situation the function models and in terms of its graph or a table of values. Analyze and explain the key characteristics of the graph of a linear function.

Distinguished

Construct, graph, and analyze linear and nonlinear functions; solve realistic problems and interpret functions in terms of the situations they model; and explain key features of linear functions written in various algebraic forms to describe applicable situations.