IB Math AI SL 2.4 – Key Features of a Graph

Topic: Functions
Level: IB Mathematics: Applications and Interpretation (SL)
File Type: Editable PowerPoint / Lesson Slide Deck

Overview

This lesson teaches students how to identify and interpret the key features of a graph, a core skill in IB Mathematics: Applications and Interpretation. Students learn how to recognize and label maximum and minimum points, intercepts, endpoints, and asymptotes, as well as determine intersections between graphs using technology.

The presentation combines conceptual understanding with practical graphing techniques, emphasizing clear, labelled sketches and the distinction between sketching and drawing as defined by the IB.

Learning Objectives

By the end of this lesson, students will be able to:

• Identify key features of a graph, including:

  • Maximum and minimum points
  • x- and y-intercepts
  • Endpoints
  • Asymptotes (vertical and horizontal)

• Find the points of intersection between two functions using technology.

• Distinguish between sketching (general shape and features) and drawing (accurate, to-scale diagrams).

• Label and interpret graph features correctly when sketching by hand or using digital tools.

What’s Included

• Step-by-step examples of identifying intercepts, maxima, minima, and asymptotes.
• Visual comparison of “Sketching vs Drawing” with IB-aligned definitions.
• Guided practice finding intercepts and intersection points using a calculator or software.
• Real-world example: analyzing and comparing two functions on the same axes.
• Tips for presenting graphs clearly in IB assessments.

Lesson Highlights

• Key Features Defined: Students explore how each element (intercepts, asymptotes, extrema) contributes to understanding graph behavior.
• Practical Application: Sketching functions such as ( f(x) = 4x^{-2} - 1 ) and ( g(x) = x^2 ), then analyzing intersections and asymptotes.
• Technology Integration: Using a graphing calculator or software to confirm analytical solutions.
• IB Exam Connection: Reinforces command terms and expectations for graph sketching accuracy and feature labelling.

Why You’ll Love It

• Builds essential graph interpretation skills for all later calculus and modeling topics.
• Integrates manual graph sketching with technology-based validation.
• Fully aligned with IB Math AI SL Topic 2.4 – Key Features of a Graph.
• Visually clear, conceptually focused, and editable for classroom or online teaching.
• A perfect continuation of the Functions unit (SL 2.1–2.3) and preparation for calculus.

Tags

IB Math AI SL, Functions, Key Features of a Graph, Intercepts, Asymptotes, Maximum and Minimum Points, Sketch vs Draw, Graphing, IB Curriculum, Lesson Slides, Editable PowerPoint