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.
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.
Interpreting Scatterplots
Given scatterplots that represent problem situations, the student will determine if the data has strong vs weak correlation as well as positive, negative, or no correlation.
Making Predictions and Critical Judgments (Table/Verbal)
Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.
Collecting Data and Making Predictions
Given an experimental situation, the student will write linear functions that provide a reasonable fit to data to estimate the solutions and make predictions.
Writing Expressions to Model Patterns (Table/Pictorial → Symbolic)
Given a pictorial or tabular representation of a pattern and the value of several of their terms, the student will write a formula for the nth term of a sequences.
Analyzing the Effects of the Changes in m and b on the Graph of y = mx + b
Given algebraic, graphical, or verbal representations of linear functions, the student will determine the effects on the graph of the parent function f(x) = x.
Writing Equations of Lines
Given two points, the slope and a point, or the slope and the y-intercept, the student will write linear equations in two variables.
Predicting, Finding, and Justifying Data from an Equation
Given data in the form of an equation, the student will use the equation to interpret solutions to problems.
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.