Function Foundations

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 you'll learn in this lesson

Inside the lesson — a free preview

Relations & Functions

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.

A. Linear Function: y = x

Graph Characteristics.

Domain.

Range.

B. Quadratic Function: y = x²

Graph Characteristics.

Domain.

Range.

C. Polynomial Function (Cubic): y = x³

Graph Characteristics.

Domain.

Range.

D. Radical Function (Square Root): y = √x

Graph Characteristics.

Domain.

Range.

E. Reciprocal Function: y = 1/x

Graph Characteristics.

Domain.

Range.

F. Absolute Value Function: y = |x|

Graph Characteristics.

Domain.

Range.

Vertical Line Test

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.

Function Notation

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?

📝 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. Interval notation uses brackets to describe a range of numbers. There are two rules.

Rules.

Worked example: Worked Examples

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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