Math Antics: Algebra Basics - Functions
Introduction to Functions
- Function: In math, a function relates or connects one set to another set in a particular way.
- Set: A collection of things, often numbers, but can be letters, names, etc.
- Can have finite or infinite elements.
Components of a Function
- Input Set: Called the domain.
- Output Set: Called the range.
- Functions relate each value from the input set to a value in the output set.
Function Tables
- Used to list inputs and corresponding outputs.
- Function is often shown as a mathematical rule or procedure above the table.
Examples of Functions
- Polygon Example
- Input: Polygon names (Triangle, Square, etc.)
- Output: Number of sides
- Algebraic Example: y = 2x
- Input values: 1, 2, 3
- Outputs: 2, 4, 6 (y = 2x)
Function Limitations
- One-to-Many Relations: Functions cannot have one input relate to multiple outputs.
- Equation y² = x shows this limitation.
Identifying Functions
- One-to-One Relation: A function must relate each input to exactly one output.
- Vertical Line Test
- Used to determine if a graph represents a function.
- If a vertical line intersects a graph at more than one point, it is not a function.
Graphs of Functions
- Functions can be graphed on a coordinate plane.
- Linear Functions: Example, y = x + 1 forms a straight line.
- Other function types: Quadratic, cubic, trig functions.
Function Notation
- Commonly written as f(x) instead of y.
- f(x): Represents a function named f with input x and output y.
- Not a multiplication; f is not a variable.
- Highlighting function usage over an equation.
- Useful for evaluating specific values of x (e.g., f(4) for specific input).
Recap
- Functions relate inputs to exactly one output.
- Domain: Set of all input values.
- Range: Set of all output values.
- Functions can be graphed as ordered pairs.
Conclusion
- Basic introduction to functions.
- Encouragement to practice and learn more about functions in algebra.
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