Unit 3: Rational Functions
Graphing Rational Functions Using Key Characteristics
Date: _
L.G.: I can sketch a rational function by using its key characteristics (domain, range, intercepts, asymptotes, intervals of
increase/decrease, and symmetry).
Definit
MHF4U
Date: _
Double Angle Formulas
L.G.: I can verify and use the double angle formulas.
Using your knowledge of compound angles, determine the following Double Angle Formulas:
Sine Double Angle Formula
Cosine Double Angle Formula
Tangent Double Angle Fo
Unit 5: Trigonometric Functions
Date: _
L4: Graphing Transformations of Sinusoidal Functions
L.G.: I can sketch sinusoidal functions in radian measure using transformations.
Recall: General Transformation Equation
Function
y
y
a sin k x h
c
State the ampl
MHF4U
Date: _
Compound Angle Formulas
L.G.: I can verify and use the compound angle formulas.
The Development of the Cosine compound angle formula
i)
ii)
iii)
iv)
v)
Consider the unit circle. Draw in two terminal arms corresponding to angles a and b.
Crea
Unit 3: Rational Functions
Date: _
Extra Insert: The Limiting Value of a Function
Minds On: What happens to the value of a function f, as x gets closer and closer to a particular value of a? Does f(x) tend
to home in on some specific value, that is, does
Unit 5: Trigonometric Functions
Date: _
L1: Radian Measure
L.G.: I can use radian measurement to represent the size of an angle.
What is a RADIAN?
Definition of a Radian
Radians are an alternative way to measure angles, other than using degrees. The numbe
Unit 5: Trigonometric Functions
Date: _
L2: Radian Measure and Angles on the Cartesian plane
L.G.: I can evaluate the trigonometric ratios for angles between 0 and 2.
Degrees vs. Radians
Special Angles
Special triangles can be used to determine the exact
MCR 3UI
Date: _
L#3: The Parent Sinusoidal Functions
L.G.: I can sketch the parent functions of sine, cosine, and tangent using radian measure.
Part I: The Sine Function: For the following values of x, determine the value of sinx. Complete the table below
Unit 3: Polynomial Functions
Lesson #3: Characteristics of Polynomial Functions in Factored Form
Date: _
L.G: I can sketch the graph of a polynomial function given in factored form using its key features as well as
determine the equation of a polynomial g
Unit 3: Rational Functions
Date: _
Solving Rational Equations
L.G.: I can solve simple rational equations in one variable algebraically, and verify solutions using technology.
Warm Up: Solve the following equations:
a)
b)
Success Criteria for solving Rati
Unit 2: Polynomial Functions Investigation
Function
Degree
Equation and sketch of the Graph
1. y
2. y
2x
3
2x 1
3. y
x2
4. y
3x 2
5. y
(x
6. y
or y
2 x( x 3)
2x 2 6x
7. y
2
2) 2
x3
8. y
( x 2)(x 1)(x 3) or
3
y
x 2 x2 5x 6
9. y 2 x( x 2) 2
or y 2 x 3 8 x 2
Review of the Reciprocal Function and its Transformations
1
and state the following:
x
Domain :
Graph f ( x)
Range:
Asymptotes:
Intervals of Increase:
Intervals of Decrease:
Transformations of f ( x)
1
x
For each transformations of y 1 , identify the tran
Unit 3: Rational Functions
Solving Rational Inequalities Graphically or Algebraically
Date: _
L.G.: I can solve a rational inequality both algebraically and by graphing.
Minds On:
Solve
a) Graphing: let f ( x)
x
1
x
x and g ( x)
1
x
b) Algebraically Note
Unit 2: Polynomials
Date: _
Lesson 8: Solving Polynomial Equations
L.G.: I can use factoring skills to solve polynomial equations and problems involving polynomials
Minds On: A rectangular sheet of metal with dimensions 30cm by 20cm is to be used to creat
Unit 2: Polynomials
Date: _
Lesson #5: Dividing Polynomials
L.G.: I can divide one polynomial by another polynomial to determine the quotient and the remainder.
Warm Up: Divide the following numbers using long division. Highlight the quotient and remainde