The Remainder Theorem
If the polynomial function f(x) is divided by ( x - c ) then the remainder is equal to f(c).
ex.
evaluate f(x) = x³ - 3x² + 2x -1 at f(3) by synthetic division and the
remainder theorem.
Algebra
Forum reference:
Book page:
http://course-notes.org/Algebra
Synthetic Division
ex.
divide (2x4- 5x3+ 7x2+ 3x + 2) by (x - 3)
Inverse Functions
The inverse of (a,b) is (b,a).
Functions are said to be inverse of each other if f o g = g o f.
Finding Inverse Functions
Adding, Subtracting, Multiplying and Dividing Functions
( f + g )(x) = f(x) + g(x)
( f - g )(x) = f(x) - g(x)
Composite Functions
(f o g) (x) = ( f (g(x) ),
The domain of f o g such that x is in the domain of g and that g(x) is the domain of f.
ex.
Relations and Functions
A set of ordered pairs is called a relation.
ex.
(1,2), (3,5), (7,10)...are relations.
The first components in the ordered pairs (x-coordinate) is called the domain, and the second components (y-coordinate or f(x) coordinate) is called the range.
Translation of Axes - Hyperbola
Standard Equation for Hyperbolas:
Translation of Axes
The general equation for conic sections is :
Ax2 + By2 + Dx + Ey + F = 0
Other Types of Graphs
To Translate the Graph:
ex.
(y - k) = | ( x - h) |
Replace (x - h) with x' and (y - k) with y':
Graph the equation with x' and y' with (h,k) as the center or vertex:
y' = | x' | at (h,k)
Symmetry
Y-axis symmetry:
The graph of an equation is symmetric with respect to the y-axis if an equivalent equation is obtained when x is replaced by -x.
Pages
Need Help?
We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.
For general help, questions, and suggestions, try our dedicated support forums.
If you need to contact the Course-Notes.Org web experience team, please use our contact form.
Need Notes?
While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!
