Unit 1: Relations, Functions & Graphs
After completing this unit you must be able to:
 Determine whether a given relation is a function
 Perform operations with functions.
 Evaluate and find zero’s of linear functions
 Graph and write functions and inequalities
 Write equations of parallel and perpendicular lines
 Model data using plots and write prediction equations
 Solve systems of equations and inequalities
 Define matrices
 Add, subtract, and multiply matrices
 Use matrices to model transformation
 Find determinants and inverses of matrices
 Graph functions, relations, inverses and inequalities
 Analyze families of graphs
 Investigate symmetry, continuity, end behavior, and transformations of graphs
 Find asymptotes and extrema of functions
 Solve problems involving direct, inverse and joint variation
 Determine roots of polynomial equations
 Solve quadratic, rational, and radical equations and inequalities
 Find the factors of polynomials
 Approximate real zeros of polynomial functions
 Write and interpret polynomial functions that model realworld data.
Essential Questions
How do we model data from realworld applications?

How do we graph, manipulate, and solve polynomials?

How do we graph, manipulate, and solve linear equations and systems?

Why should we care about graphs?

What are matrices good for?

Key Vocabulary
Relation
Functions Composite Function Standard form Slopeintercept form Pointslope form Scatter plots Piecewise function Inverse matrix Additive identity matrix Translation matrix Elimination method Absolute maximum Absolute minimum Constant function Asymptotes Constant of variation Continuous Direct variation Discontinuous End behavior Even function Completing the square Complex number Conjugate Extraneous solution Factor theorem 
Domain
Range xintercept yintercept Model Regression line Goodness of fit Absolute value function m x n matrix Rotation matrix Square matrix Vertex theorem Extrema Horizontal asymptote Inverse function Point symmetry Point of inflection Point of discontinuity Inversely proportional Inverse relations Joint variation Jump discontinuity Line symmetry Integral root theorem Leading coefficient Synthetic division Quadratic Formula 
Horizontal line test
Vertical line test Slope Zeros of a function Prediction equation Bestfit line Greatest integer function Step function Determinant Reflection matrix Substitution method Transformation Relative extrema Monotonicity Odd function Parent graph Critical point Slant asymptote Vertical asymptote Rational root theorem Remainder theorem Root Partial fractions Polynomial equations Descartes’ Rule of signs Discriminant Imaginary number 
Schedule
811 Monday
813 Wednesday 815 Friday 818 Monday 820 Wednesday 825 Monday 827 Wednesday 829 Friday 91 Monday 93 Wednesday 
Intro to the Class, Assignment 1, reviewed algebra concepts
Assignment 1 due, review composite functions, absolute value functions, start Assignment 3 Assignment 3 due, review scatterplots and regression lines, Assignment 2 Nothing due. Work on regression lines and correlation coefficients. Assignment 2 due next class. Assignment 2 due. Work on solving systems of equations using graphing calculators, elimination method, and substitution method. Begin InClass 2 and InClass 3. InClass 2 and InClass 3 due. Notes on matrices, adding, subtracting, and multiplying. Begin working on Assignment 4. Assignment 4 Due. Begin work on Assignment 5. Inverse Matrices, Solving with a calculator. Finish Assignment 5. Work on Assignment 6 review. Assignment 6 due. Begin work on Assignment 7. Review for quiz. Quiz #1 

Assignments

