Lesson 3: Getting Information from the Graph of a Function

What information can we determine by examining the graph of a function?

How can we identify x-intercepts and y-intercepts from a graph?

How do we determine where a function is increasing or decreasing?

What are relative maxima and minima, and how can we identify them from a graph?

How do end behaviors describe how a function behaves as
𝑥 becomes very large or very small?

How can interpreting graphs help us understand real-world relationships?

x-intercept

y-intercept

Increasing interval

Decreasing interval

Relative maximum

Relative minimum

Turning point

End behavior

Domain

Range

Function notation

Local maximum / Local minimum

HSF-IF.B.4

Interpret key features of graphs and tables in terms of the quantities.

HSF-IF.C.7

Graph functions and show key features including:

intercepts

maxima and minima

intervals of increase/decrease

HSF-IF.B.6

Calculate and interpret the average rate of change of a function over an interval.

Lesson Description

In this lesson, students learn to interpret the graphical representation of functions to determine key characteristics and behavior.

Students will analyze graphs to determine:

Intercepts

Relative maximum and minimum values

Intervals where the function is increasing or decreasing

Overall end behavior of the function

Students will also learn how graphs provide important information about real-world situations modeled by functions.

Purpose

The purpose of this lesson is to help students develop the ability to extract meaningful mathematical information from graphs, a critical skill used throughout algebra, trigonometry, and calculus.

This section builds foundational skills needed for:

analyzing polynomial graphs

understanding transformations

interpreting real-world models

solving equations graphically


Primary Level: DOK 2 – Skills and Concepts

Support for Developing Learners

Provide labeled example graphs highlighting intercepts and extrema.

Use guided notes with partially completed graphs.

Reinforce vocabulary with visual anchor charts.

Use graphing technology to dynamically display graph features.

On-Level Strategies

Students work in pairs to analyze graphs and describe function behavior.

Practice identifying intervals of increase/decrease.

Use graph interpretation problems from the textbook.

Enrichment / Extension

Have students create functions that produce specific graph characteristics.

Analyze real-world graphs (temperature, profit models, etc.).

Ask students to determine possible equations from given graphs.

Exit slips and Quiz

textbook

• Desmos Graphing Calculator

• TI-83 / TI-84 Graphing Calculators

• SmartBoard interactive graph displays