Understand functions as set mappings, tables, and graphs. Using these tools, learn how to work with functions and transform them and their graphs. Then, use the framework of functions to do a deep dive on quadratics. You'll explore factoring, completing the square, learn about polynomials, and eventually develop the quadratic equation.
Overview
Syllabus
- Introducing Functions: Learn what a function is, and how it relates to tables and graphs.
- What is a Function?: Discover the inputs and outputs of functions.
- Tables and Graphs: Use functions to create tables and graphs.
- Domain and Range: Identify the possible inputs and outputs for functions.
- Working with Functions: Build fluency with functions, learning how to use and transform them.
- Rigid Transformations: Use function notation to shift graphs up, down, right, and left.
- Vertical Stretch and Shrink: Stretch, shrink, and reflects functions along the vertical axis.
- Horizontal Stretch and Shrink: Expand your understanding of transformations by stretching, shrinking, and reflecting functions along the horizontal axis.
- Quadratics: When x is squared, the function is quadratic.
- Intro to Quadratics: Get to know quadratics and their shapes.
- Factored Form: Get to the root of quadratics and investigate their factored form.
- Finding Roots: Explore various ways to factor quadratics.
- Intro to Complex Numbers: Investigate the square root of negative one and its connection to quadratics.
- Polynomials: More powers of x, more interesting functions.
- Intro to Polynomials: Get a feel for how polynomials work by interacting with their graphs.
- Arithmetic and Finding Roots: Explore factoring polynomials through arithmetic, grouping, and long division.
- Symmetry and Roots in Graphs: See how symmetry reveals the number of roots.
- Rational Functions: Divide by a polynomial to get a rational function.
- Direct and Inverse Variation: When one variable goes up, does the other go up with it?
- Variation with Powers: Explore what variation looks like when larger powers are involved.
- Rational Functions and Domain: Meet rational functions, and see how some inputs can make things go wrong.
- End Behavior: Make the inputs really large and see what happens.
- Problem Solving: Challenge your intuition of rational functions.
- Piecewise Functions: For when a function has more than one piece.
- Absolute Value: It's always positive!
- Piecewise Functions: Splice multiple functions together to make new ones.
- Floor and Ceiling: Explore functions defined by rounding.
- Problem Solving: Stretch your understanding of piecewise functions.
