Review function basics and notation. Grade 12 Math 30-1 Alberta - essential diploma prep.
Lesson 1.1 of Function Transformations & Operations in Math 30-1 — Alberta curriculum lessons.
What is a Relation?. A relation is a set of ordered pairs, or in other words, just a number of points in a coordinate plane.
What is a Function?. A function is a special type of relation in which every value of x has only one corresponding value of y.
Domain & Range.
Graph Characteristics.
Domain.
Range.
Graph Characteristics.
Domain.
Range.
Graph Characteristics.
Domain.
Range.
Graph Characteristics.
Domain.
Range.
Graph Characteristics.
Domain.
Range.
Graph Characteristics.
Domain.
Range.
What is the Vertical Line Test?. The vertical line test is a visual method to determine if a graph represents a function.
How It Works.
Why Does This Work?. Remember: a function has only one output for each input. If a vertical line (representing a single x-value) crosses the graph twice, that means one input has two outputs — which violates the definition of a function!
Examples.
What is Function Notation?. Consider the function: y = 2x^2 + 1
A Better Way to Write This. An easy way of writing this is using function notation:
Rewriting Functions. We can rewrite the function as:
📝 What is Notation?. When describing where a function exists, we need a way to write ranges of numbers clearly and quickly. You already know how to write inequalities — notation is just a shorter, cleaner way to say the same thing:
Three Ways to Write the Same Thing.
💡 Remember. They all say the exact same thing — you need to know all three.
📊 Interval Notation. Interval notation uses brackets to describe a range of numbers. There are two rules.
Rules.
Example 1. Write x ≥ -3 in both notations.
Example 2. Write (-5, 2] as an inequality and in set notation.
Example 3. Write \ x -4 ≤ x < 7, x R \ in interval notation.
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