Working with Literal Equations
The lesson will provide a conceptual basis for illustrating the parallelism between solving multi-step equations and translating literal equations into solutions for specified variables.
6 OnTRACK Algebra I: Properties and Attributes of Functions
Students will learn how to use the properties and attributes of functions.
Transformations of Absolute Value Functions
Given an absolute value function, the student will analyze the effect on the graph when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values.
Kid2Kid: Determining the Meaning of Slope and Intercepts
Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish
Domain and Range: Numerical Representations
Given a function in the form of a table, mapping diagram, and/or set of ordered pairs, the student will identify the domain and range using set notation, interval notation, or a verbal description as appropriate.
Transformations of Square Root and Rational Functions
Given a square root function or a rational function, the student will determine the effect on the graph when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values.
Transformations of Exponential and Logarithmic Functions
Given an exponential or logarithmic function, the student will describe the effects of parameter changes.
Solving Square Root Equations Using Tables and Graphs
Given a square root equation, the student will solve the equation using tables or graphs - connecting the two methods of solution.
Functions and their Inverses
Given a functional relationship in a variety of representations (table, graph, mapping diagram, equation, or verbal form), the student will determine the inverse of the function.
Rational Functions: Predicting the Effects of Parameter Changes
Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.
Writing Equations to Describe Functional Relationships (Table → Equation)
Given a problem situation represented in verbal or symbolic form, the student will identify functions.
Writing Verbal Descriptions of Functional Relationships
Given a problem situation containing a functional relationship, the student will verbally describe the functional relationship that exists.
Writing Inequalities to Describe Relationships (Graph → Symbolic)
Given the graph of an inequality, students will write the symbolic representation of the inequality.
Writing Inequalities to Describe Relationships (Symbolic → Graph)
Describe functional relationships for given problem situations, and write equations or inequalities to answer questions arising from the situations.
Connecting Multiple Representations of Functions
The student will consider multiple representations of linear functions, including tables, mapping diagrams, graphs, and verbal descriptions.
Writing the Symbolic Representation of a Function (Graph → Symbolic)
Given the graph of a linear or quadratic function, the student will write the symbolic representation of the function.
Determining Parent Functions (Verbal/Graph)
Given a graph or verbal description of a function, the student will determine the parent function.
Determining Reasonable Domains and Ranges (Verbal/Graph)
Given a graph and/or verbal description of a situation (both continuous and discrete), the student will identify mathematical domains and ranges and determine reasonable domain and range values for the given situations.
Interpreting Graphs
Given a graph, the student will analyze, interpret, and communcate the mathematical relationship represented and its characteristics.
Solving Quadratic Equations Using Algebraic Methods
Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.