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Real Functions and their Graphs
(x) of x under f is called the value of 'f ' at x. Types of Function and their Graphs: Constant function, Identity function, Polynomial function, Modulus function, Square root function, Greatest integer function or Step function (Floor function), Smallest integer function (Ceiling functio..
Graph of Logarithmic Function
Graph of Logarithmic Function - For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined. \ x g log x is a well-defined function from (0, ) to (- , ). The value of e to one place of decimal i..
Graph of Logarithmic Function - For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined. \ x g log x is a well-defined function from (0, ) to (- , ). The value of e to one place of decimal i..Graph of Exponential Function
We see that as x increases, the value of e x also increases indefinitely. Also, as x decreases, the value of e x tends toward zero. The function e x is one-on..
We see that as x increases, the value of e x also increases indefinitely. Also, as x decreases, the value of e x tends toward zero. The function e x is one-on..Graph of Logarithmic Function
For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined. \ x g log x is a well-defined function from (0, ) to (- , ). The value of e to one place of decimal is 2.7. The approximate values of the function log x for some of the values of x are as follow..
For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined. \ x g log x is a well-defined function from (0, ) to (- , ). The value of e to one place of decimal is 2.7. The approximate values of the function log x for some of the values of x are as follow..Conclusion
In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions...
Asymptotes
Any curve or straight line whose distance to a given curve tends to a given curve tends to zero is known as asymptote. An asymptote may or may not meet the curve. It acts as the boundary for the graph of a function and helps in graphing the functio..
Curve Sketching
The graph of a given function gives a visual presentation of the behaviour of the function involving a study of symmetry, rise and fall, region of existence, passage through specific points etc. The following points are helpful to trace the curv..
Constant function
A function f : A B Such that A, B R, is said to be a constant function if there exist K B such that f(x) = k. Domain = A Range = {k} The graph of this function is a line or line segment parallel to x-axis. Note that, if k>0, the graph B is above X-axis. If k<0, t..
A function f : A B Such that A, B R, is said to be a constant function if there exist K B such that f(x) = k. Domain = A Range = {k} The graph of this function is a line or line segment parallel to x-axis. Note that, if k>0, the graph B is above X-axis. If k<0, t..Inverse functions
Inverse functions are sin - 1 x, cos - 1 x, tan - 1 x etc. The graph of these functions have been done in class X..
Functions Limits and Continuity
The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the field. We connect the plotted poi..
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