Graph Functions Graph Functions In mathematics, the graph of a function f is the collection of all ordered pairs (x, f(x)). In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is sometimes referred to as curve sketching. If the function input x is an ordered pair (x1, x2) of real numbers, the graph is the collection of all ordered triples (x1, x2, f(x1, x2)), and its graphical representation is a surface. The graph of a function on real numbers is identical to the graphic representation of the function. For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e.g., the closed graph theorem in functional analysis.
Know More About :- Prime Factoring Calculator
Tutorcircle.com
Page No. : 1/4
The concept of the graph of a function is generalized to the graph of a relation. Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different codomain could have the same graph. General concept of a graph is characterized by graph of relation. A function is always recognized by its graph but they are not same because it happens that two Functions that have different co- domain must have same graph. If we test graph of a function then we use vertical line test and if we test whether function is one – to – one then we use horizontal line test. If we have Inverse Function then graph of inverse function can be obtained by plotting graph of function along the line v = u. (here 'u' is along x - axis and 'v' is along y – axis. In a graph a curve is one – to – one function if and only if it is a function. Now we will try to understand Graphing and functions with help of an example. Suppose we have a function: y = x – x2, we can plot graph of this function as shown below. We need to follow some steps for Graphing Functions: Step 1: Our function here is y = x – x2. Step 2: We assume different values of x – coordinate to find values of y – coordinate.
Learn More :- Equation of Straight Line with Slope
Tutorcircle.com
Page No. : 2/4
If we value of x – coordinate as '0' then we get the value of y – coordinate as '0'. In same way if we put value of x – coordinate as -2, -1, 1, 2, 3 then we get value of y – coordinate as -6, -2, 0, -2, -6 respectively. The graph of a function is contained in a cartesian product of sets. An XY plane is a cartesian product of two lines, called X and Y, while a cylinder is a cartesian product of a line and a circle, whose height, radius, and angle assign precise locations of the points. Fibre bundles aren't cartesian products, but appear to be up close. There is a corresponding notion of a graph on a fibre bundle called a section
Tutorcircle.com
Page No. : 2/3 Page No. : 3/4
Thank You For Watching
Presentation