# Precalculus

by
**Hayleyliz4535**

Last updated 6 years ago

** Discipline: **

Math ** Subject: **

Pre-Calculus
** Grade:**

10

Vocab1)Domail:The set of all input values for a function2)Range: The set of all output values cooresponding to elements in the domain3)Function: A relation that associates each value in the domain with exactly one value in the range4)Continuous Function: A function that is continuous on its entire domain5)Bounded: A function f is bounded if there are numbers b and B such that b is less than or equal to f(x) which is less than or equal to B for all x in the domain of f6) Bounded Below: A function f is bounded below if there is a number b such that b is less than or equal to f(x) for all x in the domain of f 7) Bounded Above: A function f is bounded above if there is a number B such that f(x) is less than or equal to B for all x in the domain of f8) Local Extrema: A local maximum or minimum9)Absolute Extrema: minimum or maximum value 8)Symmetry: The graph "looks the same" when viewed in more than one way9)Asynptotes: Describes the behavior of the graph at its horizontal or vertical extremities

Sections 1.1, 1.2, 1.3

PreCalculus H:HayleyJohnson

Modeling and Equation Solving

Section 1.1

Vocab:1) Mathematical Model: A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior.2) Numerical Model: A model determined by analyzing numbers or data in order to gain insight into a phenomenon.3) Algebraic Model: An equation tha relates variable quantities asociated with phenomenon,4)Graphical Model: A visible representation o fa numerical or algebraic model5)Zero Factor Property: If ab=o, then either a=0 or b=06) Grapher Failure: Occasionally graphing calculators and programs can produced graphical models that can misrepresent the phenomena we wish to study, this is called grapher failure.7) Hidden Behavior: Sometimes the viewing window will be too large, obscuring details of the graph which we call hidden behavior8) Deductive Reasoning: The pprocess of utilizinf feneral info to prove a specific hypothesis

Real World Applications*Mathmatical Models are now a big field itself. These models can be used to figure out statictis, to show relations, explain scientific reasearch, etc. * Polya's problem solving steps are useful in many ways. In more than in just math, its explains logically ways that you can interperet and work through problems and experiences.

http://www.zweigmedia.com/RealWorld/tutorialsf0/framesF1A.htmlhttp://www.mathsisfun.com/algebra/zero-product-property.htmlhttp://www.hawaii.edu/suremath/why1Polya.htmlhttp://frewin.weebly.com/precalculus-modeling-with-functions.html

Section 1.2

Real World:Asymptotes are used in real life to find what something cannot equal. This is used in many science reaserc, and equations companies formulate to find values that are explicit.Knowing the properties of graphs is an important thing to know especially dealing with satitstics. This can help predict an outcome or parts of data.

Functions and Their Properties

http://education-portal.com/academy/lesson/analyzing-the-graph-of-a-rational-function-asymptotes-domain-and-range.html#lessonhttp://www.mathsisfun.com/algebra/rational-expression.htmlhttp://www.brightstorm.com/math/calculus/limits-and-continuity/continuity/allhttp://www.millersville.edu/~bikenaga/calculus/incdec/incdec.html

Section 1. 3

12 Basic Functions

Vocab1) Identity Function: The funchtion of f(x)=x2) Squaring Function: f(x)= x squared3) Cubing Function: f(x)=x cubed4) Square Root Function: f(x)= square root of x5) Ln Function: f(x)=ln x6) Reciprical Function: f(x)= 1/x7) Exponential Function: f(x)= e to the x8) Sine Function: f(x)= sin x9) Cosine Function: f(x)= cos x10) Greatest Integer Function: f(x)= int x11) Absolutte Value Function: f(x)= abs (x)12) Logistic Function: f(x)= 1/ 1 + e to the -x

http://education-portal.com/academy/topic/functions-basics-for-precalculus-tutoring-solution.htmlhttp://www.shelovesmath.com/algebra/advanced-algebra/parent-graphs-and-transformations/http://www.sophia.org/tutorials/precalc-lesson-13-and-16-twelve-basic-functions-anhttps://jeopardylabs.com/play/chapter-11-139

Real World Ex.* Graphs are used everyday. Exponential and logistic graphs are used a lot to show the growth of population and the growth of an area.* Many engineering and sciences use the radical function, for an example, voltage

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