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# 2022 A1-F-1-2

last edited by 1 year, 2 months ago

A1.F.1.2

A1.F.1.2 Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.

## In a Nutshell

Students will understand that the independent variable and domain refer to the x- (or input) values of a relation or function and the dependent variable and range refer to the y- (or output) values of a relation or function. With function notation, students will understand f(x) is the dependent variable (or output), as it changes with x, the independent variable (or the input). Restrictions may occur when x- and/or y-values do not exist in a real-world context.

## Teacher Actions

• Develop a deep and flexible conceptual understanding by examining patterns of how an output (y-value) is affected when input (x-values) vary for a specific function.

• Develop the ability to communicate mathematically by interpreting and translating functions both verbally and graphically and discussing independent and dependent variables and their restrictions in certain contexts.

• Provide mathematical representations of various models of functions and allow the students to make connections between the domain(x-values) and how it affects the range(y-values).

• Facilitate meaningful mathematical discourse by allowing opportunities for students to compare and explain the reasoning for determining the dependent and independent variables as expressed in the real-world situation, or in a graph.

• Pose purposeful questions supporting student exploration of domain, range, and their restrictions.

• Elicit and use evidence of student thinking as students provide a written or verbal description and/or visual model to explain their understanding of variables and how to identify restrictions.

• Support productive struggle by allowing various ways for students to demonstrate an understanding of the independent and dependent variables in real-world situations.

## Misconceptions

• Domain is the set of x-coordinates within a set of points on a graph or within a written set of ordered pairs. These values are the input to a function or relation.

• Range is the set of y-coordinates within points on a graph or within a written set of ordered pairs. These values are the output of a function or relation.

• The independent variable is the variable whose value determines the value of other variables.

• Example: In the formula for the area of a circle, A = πr2, r is the independent variable, as its value determines the value of the area (A).

• The dependent variable is the variable whose value is determined by the change in the value of an independent variable.

• Example: In the formula for the area of a circle, A =πr2, A is the dependent variable, as its value depends on the value of the radius (r).

• Any linear function will not have restrictions on its domain and range in a general context.

• Restrictions on the domain and range of an absolute value function are determined by the location of its vertex.

• Students misidentify the dependent and independent variables.

• Students may not identify restrictions on domain and range for a variety of mathematical situations involving graphs, equations, and/or real-world contexts.

• Students may not correctly identify the domain and range represented in a context of a mathematical model.

• Students struggle with determining the domain and range by assigning x-values of a function to the range and/or assigning the y-values to the domain.

## Prior Knowledge

• Recognize a function is a relationship between independent and dependent variables (PA.A.1.1)

• Identify and write the domain and range of various functions using different writing techniques and evaluating a function at any point in its domain (A2.F.1.1)

Introduction to the OKMath Framework

Algebra 1 Introduction