CENTRE DUFFERIN DISTRICT HIGH SCHOOL
MHF 4U – GRADE 12 UNIVERSITY MATHEMATICS
(1) CHARACTERISTICS OF FUNCTIONS
UNIT OUTLINE
UNIT GOALS:
You will be able to:
 Review and consolidate you knowledge of the properties and characteristics of functions and their inverses.
 Review and consolidate your knowledge of graphing functions using transformations.
 Investigate characteristics of piecewise functions.
 Calculate and interpret the average rate of change of a function over a given interval.
 Estimate and interpret the instantaneous rate of change of a function at a given point.
1.
Definition of Functions
Learning Goal:
Date(s):
We will be able to represent and describe functions.
Success Criteria:
Practice Problems:
p. 11 – p. 13:
1, 3 – 8, 12, 14.
Sample Problem:
2.
Self-Regulation:
Absolute Functions
Learning Goal:
Date(s):
We will describe and apply the properties of the absolute value function.
Success Criteria:
Practice Problems:
p. 16:
1–8
Sample Problem:
Self-Regulation:
3.
Properties of Graphed Functions
Learning Goal:
We will be able to compare various types of functions based on specific graphical
properties
Success Criteria:
Date(s):
Practice Problems:
p. 23 – p. 25:
4 – 8, 10, 15 – 16
Sample Problem:
4.
Self-Regulation:
1st Mid-Unit Review
Learning Goal:
We will apply previously learn function characteristics to different situations to surface
any misconceptions for the first part of this unit.
Success Criteria:
Date(s):
Practice Problems:
p. 28:
1–9
Sample Problem:
5.
Self-Regulation:
Sketching Graphs of Functions
Learning Goal:
We will apply transformations to parent functions, and use a variety of methods to
sketch graphs of these child functions.
Success Criteria:
Date(s):
Practice Problems:
p. 35 – p. 37:
1, 4 – 6, 8 – 11, 13,
Sample Problem:
Self-Regulation:
6.
Inverse Relations
Learning Goal:
We will determine various representations of inverse functions and the conditions
required for an inverse relation to be a function.
Success Criteria:
Date(s):
Practice Problems:
p. 43 – p. 45:
1 – 2, 4, 6 – 13
Sample Problem:
7.
Self-Regulation:
Piecewise Functions
Learning Goal:
Date(s):
We will describe, interpret, and graph piecewise functions.
Success Criteria:
Practice Problems:
p. 51 – p. 53:
1 – 4,5 – 8, 11,
13 – 15
Sample Problem:
8.
Self-Regulation:
2nd Mid-Unit Review
Learning Goal:
We will apply previously learn function characteristics to different situations to surface
any misconceptions for the first part of this unit.
Success Criteria:
Date(s):
Practice Problems:
p. 60 – p. 61:
1 – 21
Sample Problem:
Self-Regulation:
9.
Slope Between Two Points of a Function (Average Rates of Change)
Learning Goal:
Date(s):
We will calculate and interpret average rates of change of a function.
Success Criteria:
Practice Problems:
p. 76 – p. 78:
1, 4, 6, 9 – 11, 13, 15
Sample Problem:
Self-Regulation:
10. Slope of a One Point on a Function (Instantaneous Rates of Change)
Learning Goal:
Date(s):
We will calculate and interpret instantaneous rates of change of a function.
Success Criteria:
Practice Problems:
p. 85 – p. 88:
1, 4, 6, 7–10, 14–16
p. 91 – p. 92:
3, 4, 6
Sample Problem:
Self-Regulation:
11. Unit Review of Characteristics of Functions
Learning Goal:
We will apply previously learn function characteristics to different situations to surface
any misconceptions for this unit.
Success Criteria:
Date(s):
Practice Problems:
p. 60 – p. 61:
1 – 17
p. 116 – p. 117
1–7
12. Characteristics of Functions: Summative Assessment
Date(s):