Section 1.10 - Arithmetic combination of functions
· Find the sum, difference, quotient, product of two functions and their domain.
· Graph of the reciprocal function
· Vertical compression and elongation of a graph
· Composition of functions, domain of the composition, decomposition of functions
· Horizontal compression and elongation of graphs.
Section 1.12 - Inverse functions
· Definition of inverse function, checking if a function is one-to-one (horizontal line test)
· Finding inverse of one-to-one function, relationship between domain and range of a function and its inverse.
· Graphing inverse function (reflection over y=x)
· Algebraically check if two functions are inverses of each other.
CHAPTER 2 - ALGEBRAIC FUNCTIONS
Section 2.2 - Polynomial functions
· Definition of polynomial
· Graphing polynomials using shifts
· End behavior of polynomials
· Zeros and multiplicity of zeros
· Using the zeros (and their multiplicity) and the end behavior of the polynomial to sketch the graph and to find a possible formula for the polynomial.
· Deriving a possible formula for the polynomial given the graph.
Section 2.3 - Finding
factors and zeros of polynomials
·
Division algorithm (long division)
·
Factor theorem
·
Rational zero test
·
Factoring a polynomial completely.
Section 2.4 –
Rational functions
· Sketching graphs of rational function. Algebraically find:
(i) Vertical and horizontal asymptotes
(ii) x and y intercepts
(iii) slant asymptotes
(iv) end behavior
Section 2.6 - Complex
roots of polynomials
· Complex numbers, complex conjugate, complex arithmetic
· Fundamental theorem of algebra
· Conjugate pairs of zeros.
· Finding a possible formula for a polynomial with real coefficients, given zeros (real and complex).