S: Math 171 Volume 1
BC: I have really enjoyed the class thank you for the opportunity!!!!! | With Love, ___________ | I can honestly say that I thank you for the teaching my in the class. I gave it my all!!!!
FC: S M I L E :) | Math 171
1: The Value of Matrices | For finding Matrices I learned that there are several ways to do it one method is the calculator. Determine the rows and column and follow the directions that apply to the problem. Also with the matrices are determinants and inverse.
2: In Chapter 1 we explored important properties and formulas. Such as: distance, midpoint, equation of circle, determining the lines, and lots more. | To graph an equation is to make a drawing that represents the solution of that equation. | EOC Formula
3: Identity and Constant Function | Slope intercept- y+mx+b Motion formula- d+rt Point-Slope- y-y1+m(x-x1)
4: Laugh | M A T H 1 7 1 | A function f is said to be increasing on an open interval I , if for all a & b in that interval. af(b) | Even and Odd functions Even- if the graph of a function f is symmetric with respect to the y-axis. Odd- if the graph of a function f is symmetric with respect to the origin .
5: Lot's of Love | Piecewise is a function that sometimes defined by using different output formulas for different (pieces, parts, or domain) | Greatest Integer Function - f(x) = [[x]] The greatest integer less than or equal to x.
6: Some other interesting concepts that I have learned are: Origin- if replacing x with x and y produces an equivalent equation, then the graph is symmetric with respect to the origin. Reflections- graph of y= -f(x+d) is the graph of y=f(x) shifted left d units. graph of y= f(-x) is the reflection of the graph of y= f(x) across the y-axis. | Variations Direct Variation- is when y varies directly as the nth power of x if there is some positive constant k such that. y=kx Inverse- y varies inversely as the nth power of xif there is some positive constant k such that. y=k/x Jointly- y varies as x&z if there is some positive constant k such that. y=kxz
8: Complex numbers- i= square root of -1 and then i^2= -1 a+bi is standard form for complex numbers. Conjugate-denominator with the sign changed in the middle. | Completing the Square 1. a= must be one 2. move c to the right 3. multiply b time 1/2 and square and add to both sides 4. factor left sides combine like terms on right 5. take the sq root of both sides remember plus and minus sign 6. solve for x
9: Intermediate Value Theorm- P(a) and P(b) are of opposite sign then the functions has a real zeros between a & b. | Descartes rule of sign Let P(x) written in descending order or ascending be a polynomial function with real coefficients and a nonzero constant term. Positive and Negative real zeros. * the same as the number of variations of sign in p(x) * less than the number of variations of sign in P(x) by positive even integer * the same as he number of variations of sign in p(-x) *less than the number of variations of sign of sign in p(-x) by a positive even integer.
11: "Thank you, Mom for teaching me the most valuable of arts, the art of living." - Cicero