3rd Partial

3rd Partial

1. Topics

   • Polynomial Functions
     • monomial
       • Number or a product of numbers and variable with whole number exponents
       • polynomial
         • Is a monomial or a sum or difference of monomials, where each monomial is a term of the polynomial
     • The graphs of a PF are smooth cuver where the 0´s (or x-int) are the factors that compose the function
       • Maxima of a PF
         • Largest y-value of the function
         • Minima of a PF
           • Smallest y-value of the function
     • Behavior of a polynomial function
       • left
         • degree
           • odd
             • Opposite to right
           • even
             • =right
       • right
         • +
           • up
         • -----
           • down
   • Transformations
     • There are different type of transformations
       • f(x)+c
         • Vertical transformation
       • f(x+c)
         • horizontal
       • -f(x)
         • Reflection over x axis (vertical)
       • f(-x)
         • Reflection over y axis (horizontal)
       • If(x)I
         • Changes sign to the negatives f(x)
   • Quadratic Inequalities
     • Strategy (when having 1 variable)
       • Compare to 0 (pass all terms to one side)
         • Find the roots of the quadratic and split the number line with the critical points. If the comparison equal than they go colored if not they stay blank.
           • Check if the inequality satisfies the inequality.
     • Strategy (when having 2 variables)
       • It can be written in one of the following forms, where a,b, and c are real numbers and a isn't 0. Its solutions is a set of ordered pairs (x,y)
   • Even and Odd functions
     • f is even if f(-x)=f(x) for all x in the domain of f
       • f is odd if f(-x)=-f(x) for all x in the domain of f
     • Odd functions in graphs are doubles reflected (over x and y axis), this implies all exponents are odd and it doesn't have a constant
     • f is increasing on an interval I if f(x1) < f(x2) whenever x1<x2 in I
       • f is decreasing on an interval I if f(x1)>f(x2) whenever x1<x2 in I