Basic Definitions of Graphs of Functions:
Graph of a function: Graph of a function f is the set of all ordered pairs (x, f(x)); here x is in the domain of f.
Increasing Function: It is a function which is increasing on an open interval when the function increases (that is, positive slope) on an interval as you move from left to right.
Decreasing Function: It is a function which is decreasing on an open interval when the function drops (that is, negative slope) on an interval as you move from left to right.
Constant Function: A function is constant on an open interval when the function remains constant (that is, horizontal line segment) on an interval as you move from left to right.
Relative Minimum: The function consists of a relative minimum at x = a when the function computed at x=a is less than at any other point in the neighborhood surrounding x = a. The relative minimum is the lowest point in an open interval, however not necessarily over the whole domain. The relative minimums take place if the function is reducing to the left of the point and rising to the right of point.
Relative Maximum: The function consists of a relative maximum at x = a when the function computed at x = a is bigger than at any other point in the neighborhood surrounding x = a. The relative maximum is the maximum point in an open interval, however not necessarily over the whole domain. The Relative maximums take place if the function is rising to the left of the point and reducing to the right of point.
Greatest Integer Function: The greatest integer of a value is the maximum integer less than or equivalent to the value.
Symmetry about the y-axis: It is a relation in symmetric regarding y-axis if for each and every point (x, y) on the graph, the point (-x, y) is as well on the graph.
Symmetry about the x-axis: It is a relation in symmetric regarding the x-axis if for each and every point (x, y) on graph, the point (x,-y) is as well on the graph.
Symmetry about the origin: It is a relation is symmetric regarding the origin if for each and every point (x,y) on the graph, the point (-x,-y) is as well on the graph.
Even Function: The function is even if for each x in the domain of the function, f(-x) = f(x)
Odd Function: The function is odd if for each x in the domain of the function, f(-x) = -f(x)Vertical Line Test:
The relation is a function when all vertical lines drawn via the graph of the relation intersect in no more than one point.
The contra positive of that is frequently used.
The relation is not a function, when a vertical line intersects the graph of a relation in two or more points.
Greatest Integer Function:
The greatest integer function is frequently termed as the Integer function, and is abbreviated INT on the calculator. You might find the INT function on the calculator by going to the [Math] menu, arrowing right to the NUM option, and then selecting the INT function (it is number 5 on TI83).
The Integer function is at times termed as the step function as of the stair step result obtained when graphing it. Be sure to employ a decimal setting whenever graphing the maximum integer function or you will get weird outcomes. You might also wish to use Dot mode rather than Connected mode whenever graphing the Integer function. You can modify modes on the TI series by pressing the [Mode] key.
Mathematically, the maximum integer function is symbolized by using a double left bracket and double right bracket.
Symmetry-Odd/Even Functions:
Symmetry about y-axis:
Symmetry about the y-axis signifies that the left side of graph is a mirror image of the right side of graph. Mathematically, a relation that is symmetric regarding y-axis comprises the property that for each and every point (x,y) which is on graph, the point (-x,y) is as well on the graph. In another word, to mirror something about the y-axis, take the opposite of all x-coordinates and leave the y-coordinates only.
Symmetry about x-axis:
Symmetry regarding x-axis signifies that the bottom side of the graph is a mirror image of top side of graph. Mathematically, the relation that is symmetric regarding x-axis consists of the property that for each and every point (x, y) which is on the graph, the point (x,-y) is also on the graph. In another word, to mirror something about the x-axis, take the opposite of all y-coordinates and leave the x-coordinates only.
Symmetry about the origin:
The Symmetry about the origin signifies that for each and every point (x, y) on the graph, the point (-x,-y) is as well on the graph. Graphically, to make symmetry about the origin, take any point, draw an imaginary line via the origin, and put a point on that line at similar distance as the original point was from origin on the other side of origin.
Even Function:
The function is even when it is symmetric about the y-axis. Mathematically, as the y-coordinates (that is, the values of function) have to be equivalent, and the x-coordinates are opposite, one can write: f(-x) = f(x).
There is a reason such functions are termed as even. When you have a polynomial function in one variable, all the exponents on independent variable will be even. Keep in mind that a constant is zero power the variable and zero is even.
Odd Function:
The function is odd when it is symmetric about the origin. Mathematically, as both x-coordinate and y-coordinates are negated, one can write: f(-x) = -f(x).
There is a reason such functions are termed as odd. When you have a polynomial function in one variable, then all the exponents on independent variable will be odd. Keep in mind that a constant is zero power of the variable and will be even; therefore if there is a constant term, then it is not an odd function.
Latest technology based Algebra Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Algebra help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Algebra, project ideas and tutorials. We provide email based Algebra help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Algebra. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Algebra Homework help and assignment help services. They use their experience, as they have solved thousands of the Algebra assignments, which may help you to solve your complex issues of Algebra. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
www.tutorsglobe.com offers Object Oriented Design homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
Differential Calculus tutorial all along with the key concepts of Partial Derivatives, Exact Differential, Implicit Differential, Product of Three Partial Derivatives, Chain Rule of Partial Derivatives, Second Derivatives or Second Order Derivatives
Amphibia tutorial all along with the key concepts of Features of Amphibians, Features of Toad and Frog, Ecological Adaptation of Amphibians, Difference between Frog and Toad
www.tutorsglobe.com offers answering questions to comparing national income between countries assignment help-homework help by online economics tutors help.
tutorsglobe.com digestion assignment help-homework help by online human physiology tutors
tutorsglobe.com structure of cristae membrane assignment help-homework help by online mitochondria tutors
The Phylum Annelida tutorial all along with the key concepts of characteristics of Annelida, Diversity of annelids, Classification of annelids, Class Polychaeta, Class Oligochaeta and Class Hirudinea
tutorsglobe.com physiological effects of sleep assignment help-homework help by online sleep tutors
Take a quick look at top-rated Educational Psychology Assignment Help foe availing hassle free services round the clock.
tutorsglobe.com significance of abscission assignment help-homework help by online abscission and senescence tutors
Stereospecific Polymerization tutorial all along with the key concepts of Polymer Stereochemistry, Structural Isomerism, Orientational isomerism, Configurational Isomerism
Seriously, nobody would claim that accounting information completely meets all of the requirements of each of the several user groups.
www.tutorsglobe.com offers periodic table and its properties homework help, periodic table and its properties assignment help, online tutoring assistance, inorganic chemistry solutions by online qualified tutor's help.
tutorsglobe.com fish pond assignment help-homework help by online pisciculture tutors
a test light, voltage tester, test lamp, or mains tester is a extremely simple piece of electronic test equipment that is employed to ascertain the existence or nonexistence of an electric voltage in a piece of equipment under test.
1941940
Questions Asked
3689
Tutors
1473705
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!