Life as a Function

MHF 4U Culminating Activity

Objective:

• To consolidate the understanding of the properties of functions.
• To develop effective ways of communicating math ideas in visual and written format

Procedure:

1) Plan a graph with a life story

Identify clearly the dependent and independent variables.

The use of at least three different types of functions, which may include a polynomial function, a rational function, a sinusoidal

function, exponential function or logarithmic function.

Your graph should include at least two asymptotes (vertical, horizontal or oblique) within the rational, tangential and/or

logarithmic function.

Your graph should be continuous. Ensure to include the calculations proving that the graph is continuous at the point of joining.

One global maximum and one global minimum; and two or more local maximum/minimum points.

The story can be about your own life or the life of someone else, but it must be about the life of one person.

An equation for the function of life using piecewise function notation.

2) Write an outline

Describe the curve using important key features

3) Write a rough copy of your report

Project Report

You are expected to compile a clear and well­organized report. Your report should include:
• Cover page, including a title

• Introduction

• Description of procedure

• Presentation of the solutions with the graph

• Conclusions

Your report is to be assessed for its mathematical validity. The mathematical content of your report should besubstantial. This

report is your opportunity to demonstrate your understanding of the skills and concepts learned in this course.

Your written report should be no longer than three pages, double spaced, Times New Roman and 1’ margins.

4) Write a final copy

5) Visual presentation

• You will be responsible for presenting your graph on a standard Bristol board paper (to be given by your teacher)

• The board should contain anoutline of your investigation, and the results. It should highlight all of the key features of

the graph.

• The boardshould be decorated appropriately to the subject of the graph, and include a critical evaluation of yourmethodology

and conclusions.

MHF 4U LIFE AS A FUNCTION RUBRIC

CRITERIA Level R
(0 – 49%) Level 1
(50 – 59%) Level 2
(60 – 69%) Level 3
(70 – 79%) Level 4
(80 – 100%)
Knowledge and Understanding
-demonstrates no to negligible knowledge and understanding of mathematical concepts
-no identification or description of key features
-demonstrate limited knowledge and understanding of mathematical concepts
-missing most key features of the function, and description of key features is not complete -demonstrate some knowledge and

understanding of mathematical concepts
-identifies and describes some of the key features correctly
-demonstrates considerable knowledge and understanding of mathematical concepts
-identifies and describes most of the key features
-demonstrates thorough knowledge and understanding of mathematical concepts
-identifies and describes all key features correctly
Application -demonstrates no or negligible knowledge and skills, and makes no connections of the various mathematical concepts

relating functions
-no usage/evidence of transformations and key features to sketch the graph of the function -applies knowledge and skills, and

makes connections with various mathematical concepts relating to functions with limited effectiveness
-transformations and key features are used with limited effectiveness to sketch the graph of the function -applies knowledge

and skills, and makes connections with various mathematical concepts relating to functions with some effectiveness
-uses transformations and key features with some effectiveness to sketch the graph of the function -applies knowledge and

skills, and makes connections with various mathematical concepts relating to functions with considerable effectiveness
-uses transformations and key features with effectiveness to sketch the graph of the function -applies knowledge and skills, and

makes connections with various mathematical concepts relating to functions with a high degree of effectiveness
-uses transformations and key features with a high degree of effectiveness to sketch the graph of the function
Communication -function lacking comprehension
-no use or lacks proper use of mathematical notations, terminology and conventions
-no presentation
-function unclear and hard to understand
-uses mathematical notations, terminology and conventions with limited effectiveness
-presents functions to the class
-function lacks clarity and are difficult to understand
-uses mathematical notations, terminology and conventions with some effectiveness
-presents functions to the class with limited effectiveness -function somewhat clear and understandable
-uses mathematical notations, terminology and conventions with considerable effectiveness
-presents functions to the class with some effectiveness -function clear and understandable
-uses mathematical notations, terminology and conventions with a high degree of effectiveness
-presents function to the class with effectiveness and explains all key features
Thinking -no evidence of planning
-function missing and/or does not reflect life history appropriately
-no connection between key features and important life events
-demonstrate no to negligible mathematical skills -plans with limited effectiveness
-function does not depict life history with some accuracy
-demonstrates limited mathematical skills -plans effectiveness
-function depicts life history with some accuracy
-connections between life events and key features of the graph are somewhat appropriate
-demonstrates mathematical skills with some effectiveness -plans with considerable effectiveness
-depiction of function is mostly accurate
-appropriate connections between life events and key features of the graph
-demonstrates mathematical skills with considerable effectiveness -plans with a high degree of effectiveness
-function accurately depicts life history
-makes thoughtful connections between life events and key features of the graph
-demonstrates mathematical skills with a high degree of effectiveness