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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.
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.
Domain and Range: Verbal Description
The student will be able to identify and determine reasonable values for the domain and range from any given verbal description.
Modeling Data with Linear Functions
Given a scatterplot where a linear function is the best fit, the student will interpret the slope and intercepts, determine an equation using two data points, identify the conditions under which the function is valid, and use the linear model to predict data points.
Formulating Systems of Inequalities
Given a contextual situation, the student will formulate a system of two linear inequalities with two unknowns to model the situation.
Solving Systems of Equations Using Substitution
Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of substitution.
Solving Systems of Equations Using Elimination
Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of elimination.
Solving Systems of Equations with Three Variables
Given a system of three linear equations, the student will solve the system with a unique solution.
Solving Systems of Equations Using Matrices
Given a system of up to three linear equations, the student will solve the system using matrices with technology.
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.
Absolute Value Inequalities
This activity provides an opportunity for students to examine how to find solutions to an absolute value inequality.
Formulating and Solving Square Root Equations
This activity provides an opportunity for students to use a square root equation to model a situation and then use the model to make predictions.
Square Root Regression
This lesson is a student discovery lesson that culminates in square root regression with technology. Students will use their study of inverses, the relationship between quadratic and square root functions, their previous knowledge of regression, and determine how to find the square root regression of real-world data.
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.
Domain and Range: Contextual Situations
The student will be able to identify and determine reasonable values for the domain and range from any given contextual situation.
Domain and Range: Graphs
Given a function in graph form, identify the domain and range using set notation, interval notation, or a verbal description as appropriate.