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 real-world data.
How do we model data from real-world 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?
Additive identity matrix
Constant of variation
Completing the square
Goodness of fit
Absolute value function
m x n matrix
Point of inflection
Point of discontinuity
Integral root theorem
Horizontal line test
Vertical line test
Zeros of a function
Greatest integer function
Rational root theorem
Descartes’ Rule of signs
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 scatter-plots 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 In-Class 2 and In-Class 3.
In-Class 2 and In-Class 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.