Grade 11 Advanced Functions

Characteristics of Functions

Representing Functions

Explain the meaning of the term function, and distinguish it from a relation. Represent linear and quadratic functions using function notation, f(x) = ... Explain the meaning of domain and range, and describe them correctly, eg: $D = {x|x \in R, a \leq x < b }$ Be able to determine the domain and range of a funtion. This will probably require a review of inequalites. Use the form y=af(k(x-d))+c to graph a function based on parent function, determining equation from graphs. Be able to explain the role of a, k, d and c. Determine the inverse of a function numerically, graphically or algebraic representation. Introduce combinations of functions, f(g(x)), to allow them to do the inverse function test $f(f^{-1}(x)) = 1$ Determine the relationship between domain and range of a parent and inverse function.

Solve problems involving polynomials

determining number of roots by factoring, graphing or calculating the discriminant $\bigtriangleup = b^2 - 4ac$, min/max of quadratics, using various methods. Descarts' Rule of sign: count the number of sign changes and that ( or a multiple of 2 less ) are the number of real roots. Rational Root Theorem Tranformational relationship between families of functions (those having the same roots) Solve problems of based on intersection of linear and quadratic functions

Determining Equivalent Algebraic Expressions

Simplifying functions/rational functions, determine if two functions are equivalent. Determine $\sqrt(ab) = \sqrt(a) \times \sqrt(b)$

Trigonometric Functions

sin, cos, tan of special angles sec, csc, cot trigonometric identities repeat part 1 with $f(x)=\sin(x)$ Triganometric Graphs Triganometric graphing app
Graphing Sine Functions

Exponential Functions

power laws graph $a^x$ differentiate quadratic from exponential using rates of change repeat part 1 with $f(x)=a^x$ College Algebra - contains a series of worksheets that guides students through working with exponential and logarithmic functions

Discrete Functions

describing as f(n) or $t_n$ Fibonnacii and pascals triangle, geometric sequences and series financial applications - annuities, future value

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