Functions and Operations

📋 Course Outline

1. Relations and Functions
2. Testing Function Status
3. Domain and Range
4. Evaluating Functions
5. Operations on Functions
6. Composition of Functions

📖 1. Relations and Functions

🔑 Key Concepts & Definitions

• Relation : A set of ordered pairs (x, y).
• Function : A relation in which each value of x corresponds to exactly one value of y, so repetition of a domain element with different outputs is not allowed.

📝 Essential Points

• The ordered pairs {(0, 0), (-1, 1), (1, 1), (-2, 4), (2, 4)} form a function because no domain value is repeated with different outputs.

💡 Memory Hook

A relation pairs values; a function assigns each x exactly one y.

📖 2. Testing Function Status

★ Must-know

📌 An ordered-pair set is a function if every repeated domain value has the same corresponding output; it is not a function when one domain value is paired with different outputs.

📌 The vertical line test identifies a graph as a function when every vertical line intersects the graph at no more than one point; otherwise, the graph is not a function.

Further detail

• The Y-scan method identifies a non-function when:
  • y is missing
  • is inside the absolute value symbol
  • has an even exponent

💡 Memory Hook