Lesson 1: Functions

• Quick review of key terms:

  • Vertical line test

  • Transformation of a function

  • Domain and range of a function

  • Factoring expressions

• Defining key characteristics / properties of a function:

  • Intervals of increase / decrease

  • Odd and even functions

  • Continuous and discontinuous functions

  • End behaviour

  • Vertical and horizontal asymptote

• Determining end behavours

• Determination of these properties using examples

• Sketching graphs of functions

  • General equation of a transformed function

  • Description of x- and y- transformations

  • Solutions to worked examples

• Inverse of a relation

• Implications of reverse on the original function

• Defining Piecewise functions

  • Solution to a Piecewise function question

  • Solved application problems

Lesson 2: Operations with Functions

• Examples of solving operations with functions:

  • f(x) + g(x); f(x) – g(x); (f + g)(x); (f x g)(x); (f ÷ g)(x)

  • Solving (f + g)(x) within limits

  • Domain and range of (f + g)(x)

  • Determining table of values

  • Determining graphs of the functions

Description of the form of a polynomial function

• Identifying polynomial functions

• Characteristics of polynomial functions

• Graphs of polynomial functions

  • Shape and its relationship to degree

• Sketching polynomial functions (3 steps)

  • Understanding end behaviours for various functions

  • Understanding turning points for various functions

  • Understanding zeros for various functions

• Sample questions solved to solidify understanding

• Sample question to practice graphing polynomial functions

• More solutions to sample questions

Lesson 2: Polynomial Functions in Factored Form

• 3 key points to determine before sketching

• Sketching polynomial functions

• Sketching a cubic function with 2 zeros, order 2

• Determining a polynomial function given the graph

  • Determining domain and range

  • Sketching a graph of a different kind of polynomial function

Lesson 3: Cubic & Quartic Functions

• Example to find transformed points, given:

  • Parent function passing through 3 points

  • 2 separate transformations

• Transformation of a graph to determine roots of another

Lesson 4: Dividing & Factoring Polynomials

• Review of long division steps

• Division of a cubic polynomial by a binomial

• Synthetic Division explained:

  • Creation of a chart

  • Isolation of coefficients

  • Identifying the “k” factor

  • Dealing with missing ‘order terms’

• Determining factors of polynomials:

  • Identify “k”

  • Use Synthetic Division

• Determining whether a polynomial is divisible by a binomial expression

  • Identify “k”

  • Test for remainder of zero or

  • Substitute the value into the equation

Lesson 5: Factoring Sum & Differences of Cubes

• Recall Difference of Squares

• Recall sun and difference of cubic equations

• Examples of simple factoring questions

• Examples of more difficult factoring questions

Lesson 6: Solving Polynomial Inequalities

• 5 steps to solving Polynomial Inequalities

• Example solving a cubic inequality

  • All 5 steps carefully explained

• Example solving a quartic inequality

• Example solving a quartic inequality with missing terms

Lesson 1: Graphing Rational Equations

• Definition of a rational function

• Explanation of the characteristics of:

  • linear functions and their reciprocals

• Comparison of characteristics for linear and reciprocals

• Sample questions to check understanding

• Explanation of the characteristics of:

  • Quadratic functions and their reciprocals

• Simple example illustrated

  • Taking note of restrictions

• More challenging word problem

• Solutions for 2 rational inequality examples

• Use of inequality interval tables

Lesson 2: Graphing Rational Functions of the form ax + b/cx + d

• Explanation of a strategy for sketching

• Solved example using another strategy

• Solved example using a third strategy (intervals)

• Determination of graph

Lesson 3: Solving Rational Equations

• Simple example illustrated

  • Taking note of restrictions

• More challenging word problem explained

  • Use of inequality interval tables

• Solutions for 2 rational inequality examples

  • Use of algebraic process

  • Determination of inequality interval tables

Lesson 1: Radians

• Defining a Radian

• Converting degrees to Radians

• Converting Radians to degrees

• Radians and angles on a Cartesian Plane

  • Use of Special Triangles

• Finding Exact Values of angles

  • 3 steps for solving these questions

• Solving within limits

Lesson 2: Transformation of Sine x

• Recall general transformation equation

  • Explanation of terms

• Graphing transformational functions

• Description of steps involved

  • Determining the period & equation of axis, given the equation

  • Determining the amplitude, given the graph

  • Determining the equation of axis, given the graph

  • Sketching graph using the axis, points on axis, min. & max.

Lesson 1: Exponential Functions of the Form y = ax , a > 1

• Characteristics of graphs of exponential functions, a > 1

• Characteristics of graphs of exponential functions, 0 < a < 1

• Relationship between Exponential & Logarithmic functions, a > 1

  • Algebraically

  • Graphically (relationship explained)

  • Domain and range

• Solved sample questions for more clarification

• Evaluating logarithms

• Tips for solving

Lesson 2: Transformation of Logarithmic Functions

• Identifying the parent logarithmic function

• Identifying the transformed logarithmic function

• General equation of the transformed logarithmic function

• Explanation of terms

• Properties of transformed parent logarithmic functions

• Horizontal translations explained with graphs

• Vertical stretches / compressions explained with graphs

• Horizontal stretches / compressions explained with graphs

• Reflection in the x-axis explained with graphs

• Reflection in the y-axis explained with graphs

Lesson 3: Evaluating Logarithms

• Recall the definition of a logarithm

• Determining values of logarithms using definition

• 2 strategies for evaluating logarithms

• 3 properties of logarithms to know

• Solutions to sample questions using properties

• Solutions of questions to evaluate logarithms

• Estimating logarithms using a graph

• Estimating logarithms to 2 decimal places

Lesson 4: Laws of Logarithms

• Relationship with Exponent laws:

  • Product law

  • Quotient law

  • Power law

• Evaluating / simplifying logarithmic expressions

  • Identifying strategies to use

  • Expanding expressions before simplifying

• Description of transformations from one graph to another

  • Use of laws of Logarithms