Introduction to Functions
Connect inputs to outputs with functions.
Finding the Rule
Word Functions
Time Functions
Repeating Outputs
Deducing the Rule
Level Check
Numeric Rules
Writing Rules
Conditional Rules
Deducing Numeric Rules
Level Check
Graphing Linear Functions
Graphing Squared Functions
Graphing Absolute Value
Graphing Without an Equation
Interpreting Graphed Functions
Intercepts and Intervals
Increasing and Decreasing
Function Requirements
Vertical Line Test
Valid Functions
Valid Intervals
Discrete Functions
Depreciation Functions
Multi-Part Functions
Periodic Functions
Piecewise Functions
Discontinuities
Plotting Points
Plotting Piecewise Functions
Building Piecewise Functions
The Floor Function
The Ceiling Function
Plotting Floor and Ceiling
Repeating Functions
Periodicity
Domain
Range
Domain and Range
Reciprocal Functions
Squares and Ranges
Square Roots and Domains
Piecewise Ranges
Identifying Domain and Range
Adding Functions
Subtracting Functions
Multiplying Functions
Dividing Functions
Chaining Functions
Applying Multiple Functions
Combining Functions
Graphing Composites
Composite Domains
Vertical Shifting
Horizontal Shifting
Combining Shifts
Vertical Stretching
Horizontal Stretching
Combining Stretches
Reflection Across the x-Axis
Reflection Across the y-Axis
Composing Reflections
Reflecting and Stretching
Inverting a Function
Finding the Input
Finding the Inverse Function
Graphing Inverse Functions
Reflecting to Invert
Invertibility
Invertible Functions
Course description
We'll start by looking at a wide range of functions applied to numbers, strings of text and real world objects. We'll then explore properties of a wide range of numeric functions in the coordinate plane.
Topics covered
- Calculating the output of a function.
- Deducing a function rule from inputs and outputs.
- Function notation.
- Functions on the coordinate plane.
- Discrete and continuous functions.
- Interpreting function graphs.
- Piecewise functions.
- Domain and range.
Prerequisites and next steps
Before starting this course you should have familiarity with the coordinate plane, basic algebra and linear relationships of the form y=mx + c.