Course:MATH110/Archive/2010-2011/003/Groups/Group 06/Homework 5

No problem to anyone in the group

 Intersections of Functions
 Reading Graphs of Functions
 Distances and Lines
 Operations on graphs of functions
 Trigonometry and the Pythagorean theorem
 Areas and volumes

Some Issues

 Basic functions
 Properties of functions
 Equations
 Inequalities
 Composition of functions
 Polynomial long division
 Graphs of functions
 Construction of graphs
 Mathematical writing

Issues for Everyone

 na

Basic functions

to evaluate, simplify and manipulate basic functions which includes:

   * polynomials,
   * radical functions,
   * trigonometric functions,
   * inverse trigonometric functions,
   * exponential functions,
   * logarithmic functions,
   * absolute-valued functions,
   * functions that are constructed by additions, subtractions, multiplications, divi- sions, exponentiations and/or compositions of the above functions,
   * piecewise functions; 

Properties of functions -to find the domain, range and intercepts of a basic function (see above), and the behaviour of such a function at/near the endpoints of the domain;

Equations - to solve linear, quadratic, rational, radical, trigonometric, exponential, logarithmic, and absolute-valued equations;

Inequalities - to solve linear, quadratic, rational, radical, trigonometric, exponential and logarithmic inequalities;

Composition of functions -to construct new functions by applying function composition and identify the various functions that make up a composite function;

Polynomial long division -to perform long divisions of polynomials and write the result out, whether there is a remainder or not; Graphs of functions -to relate graphs to simple functions such as linear, quadratic, power, root, reciprocal, absolute-valued, trigonometric, inverse trigonometric, exponential, logarithmic and piecewise functions as well as equations involving circles and ellipses; i.e., plot a graph from a given equation and find the equation from a given graph; Intersections of functions -to find intersections of two or more graphs;

Reading graphs of functions -to find a value of a function from its graph and determine whether a point of given coordinates lies on the graph;

Distances and lines -to find the distance between two given points and the slope/equation of the line containing two given points;

Operations on graphs of functions -to translate, scale and reflect graphs;

Construction of graphs -to construct a graph from a given context and extract information related to a given context from a graph; Trigonometry and the Pythagorean theorem - to apply the Pythagorean theorem, write down trigonometric relationships involving the sides and angles of a right triangle, and express proportional relations between similar triangles;

Areas and volumes - to compute the area of basic 2D shapes, and the surface area and the volume of basic 3D shapes;