Embedded Files
Khan
Graphs of exponentials and logarithms
Graphs of absolute value functions
Graphs of square root functions
Graphs of trigonometric functions
Understanding linear and exponential models
Constructing linear and exponential functions
Comparing growth rates of exponentials and polynomials
Interpreting features of functions
Comparing features of functions
Shifting and reflecting functions
Modeling with exponential functions
Modeling with combined functions
These lessons will involve the students in investigating and understanding:
• How to graph functions of the form:
• ax+b where a,b ∈ Q, x ∈ R
• ax2+bx + c where a,b,c ∈ Q, x ∈ R
• ax3+bx2+cx+d where a,b,c,d ∈ Z, x ∈ R
• abx where a, b ∈ R
• logarithmic
• exponential
Project Maths
Geogebra
• That a function assigns a unique output to a given input
• Domain, co -domain and range
• The composition of functions (including the notation used)
Khan
Evaluating expressions with function notation
Evaluating composite functions
Alison Videos
Matching functions and graphs – quadratic / exponential
• How to recognise surjective, injective, and bijective functions
Alison
Inverse and bijective functions
• How to find the inverse of a bijective function and understanding that it is a function
Khan Video
Introduction to the inverse of a function
Surjective (onto) and injective (one-to-one) functions
Relating invertibility to being onto and one-to-one
Determining whether a transformation is onto
Khan
Algebraically finding inverses
Understanding inverses of functions
Positive and negative parts of functions
Recognizing features of functions
• Make use of function notation f(x) = , y = and f:x→
Khan Video
• The concept of the limit of a function where it arises • How to interpret equations of the form f(x)=g(x) as a comparison of the above functions • How to sketch the graph of the inverse of a function given the function • use graphical methods to find approximate solutions to • f(x) = 0
• f(x) = k
• f(x) = g(x)
where f(x) and g(x) are of the above form, or where graphs of f(x) and g(x) are provided
Khan
Solving systems of equations for the king
• Express quadratic functions in complete square form
• The relationship between x2, ax2, x2+ c, (x-h)2+ k, a(x-h)2+ k
Sketching functions in x direction
Sketching functions in the y direction
Khan
Shifting and reflecting functions
Practice: Transforming functions
• How to use the complete square form of a quadratic function to find the roots and turning points
• How to use the complete square form of a quadratic function to sketch the function
Alison
Completing the square and sketching the full method
Khan
Completing the square in quadratic expressions
Solving quadratics by completing the square 1
Solving quadratics by completing the square 2
Rewriting quadratic expressions to reveal key features
Graphing parabolas in standard form
Graphing parabolas in vertex form
Graphing parabolas in all forms
EXTRA
Project Maths
Shifting & Scaling Graphs - Functions
Introducing the exponential function
Extra Khan Topics
Graphing & Analysing Linear Functions
Polynomial & Rational Functions
Exponential & Logarithmic Functions
Interpreting features of functions
Comparing features of functions
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