School level

# 30th March

## 30th March:  Investigating the various types of functions

### Learning Outcomes

Students studying at OL & HL should be able to:

• recognise that a function assigns a unique output to a given input
• investigate the concept of the limit of a function
• recognise surjective, injective and bijective functions
Workshop Resources & Presentation
Teaching and Learning Plans
GeoGebra Files
Student Activities

### Using Problem Solving to Introduce Limits

(Worksheet) Investigating the change in the final value of €1, if the annual interest rate of 100% is compounded over smaller and smaller intervals.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: To introduce the concept of a limit

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Function or Relation

A matching activity looking at where identifying relations or functions based on algebraic representation and graphical representation.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Presentation
Language: English
Special Needs:

### Matching Activity Slides for Surjective, Injective and Bijective Functions

This is the slideshow to accompany the matching activity document of the same title

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Presentation
Language: English
Special Needs:

### Introducing Exponential Functions

https://www.scoilnet.ieuploads/resources/26430/26166.pdf Added: 24 Apr 2018 Contributor: PDST Resource type: Assessment / Presentation

PowerPoint to guide teachers in introducing exponential functions to students. Students will investigate the properties of exponential functions and the features of their graphs. Prior knowledge includes understanding the laws of indices and functions.

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: Introduction to exponential functions

Key Skills: Communicating Managing Information and Thinking Working with Others Literacy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Review of properties of exponential functions

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Understanding Exponential Functions

https://www.scoilnet.ie/pdst/maths/...tudent/lc/lc-functions/exponential/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra file to learn how changes to the exponential function affect its graph.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### Scaling and Shifting (Horizontally and Vertically) a Quadratic Function

https://www.scoilnet.ie/pdst/maths/...draticfunctions/shiftingandscaling/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Use this interactive file to learn how changes to a quadratic function affect its graph.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### Logarithmic Functions

https://www.scoilnet.ie/pdst/maths/...tudent/lc/lc-functions/logarithmic/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra file to learn about logarithmic functions and their graphs.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### Relationship between e^x and ln(x)

https://www.scoilnet.ie/pdst/maths/...udent/lc/lc-functions/relationship/ Added: 09 Nov 2019 Contributor: PDST Resource type:

Interactive Geogebra file to understand the relationship between an exponential function and a logarithmic function with the same base.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### Shifting and Scaling Quadratic Functions

Presentation on shifting and scaling quadratic functions including student activities. This presentation prepares students for activity on quadratic functions. The students work with the graphs different quadratic functions.

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: looking at shape of quadratic graphs and investigating changes that occur when a constant has different values.

Key Skills: Communicating Working with Others Literacy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: looking at shape of quadratic graphs and investigating changes that occur when a constant has different values.

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Graph Matching Activity on Quadratic Functions

Student activity to assess their understanding of transformations of quadratic functions and their graphs. In this activity, students match quadratic functions given in different forms such as graph, vertex form, intercept form,.

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: To assess student understanding of transformations of quadratic functions and their graphs

Key Skills: Communicating Working with Others Literacy Numeracy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: To assess student understanding of transformations of quadratic functions and their graphs

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Limits and Continuity of Functions Activities

Informal Introduction to Limits and Continuity of Functions

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: To investigate the trends in the values of different functions f(x) as x approaches a specific value.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Exploring Exponential Functions

https://www.scoilnet.ieuploads/resources/26428/26164.pdf Added: 24 Apr 2018 Contributor: PDST Resource type: Worksheet / Activity

A booklet for students to study the properties of exponential functions and explore the features of their graphs. They compare the graph of f(x) = a^x where a> 1 with the graphs f(x) = a^x where a<1 .

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: Introduction to exponential functions ( 2^x, 3^x)
Introducing graphs of exponential functions
Using exponential functions to solve real life problems

Key Skills: Communicating Managing Information and Thinking Working with Others Literacy Numeracy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Review of exponential functions ( 2^x, 3^x)
Reviewing graphs of exponential functions
Using exponential functions to solve real life problems

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Functions Matching - Injective, Surjective or Bijective

This is a matching activity that looks at establish the nature of a variety of functions.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Document
Language: English
Special Needs:

### Summary Sheet of Injective, Surjective and Bijective Functions

This sheet looks at what makes a function injective, surjective & bijective

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Document
Special Needs: # Registering for a Scoilnet Account – your first step to contributing and sharing

## What you need...

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.