Wikipedia
Graph of a function - 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..
Graph of a function - In mathematics, the graph of a function f is the collection of all ordered pair s ( 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..
TutorVista
Identify the constant function from the graphs.
Identify the constant function from the graphs. => Graph 1 or Graph 3 or Graph 2 or Graph 4..
Find the function of the graph.
Find the function of the graph. => y = | x | - 1 or y = | x | + 1 or y = x + 1 or y = - x - 1..
Which of the functions represents the graph?
Which of the functions represents the graph? => f ( x ) = x 2 - 4 or f ( x ) = x 2 + 4 or f ( x ) = 2 x 2 + 1 or f ( x ) = 2 x 2 - 8..
Real Functions and their Graphs
Real Function: A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real number..
Real Function: A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real number.. polynomial functions and their graphsDefines polynomial functions and discusses features of their graphs, such as increasing and decreasing.
Functions and Analyzing Graphs - CalculusFree calculus lecture introducing functions and analyzing the graphs they produce. Presented by www.free-academy.com
Question : Suppose f is differentiable and the graph of its derivative f ' is given. If f(0) = 1, how do I roughly sketch the graph of f???
Answer : You use a slope field. Remember: the derivative of a function at a given point is the SLOPE of the original function there. For example, if f ' (3)=7, then the SLOPE of f at 3 is also 7. So you know that f(0)=1. Look at the value of f ' (0), and make s short line segment that crosses (0,1) with that slope. Follow that line and continue on with this technique using each value (1, 2, 3, and -1, -2, -3, etc). When you're done, connect the line segments to form a continuous graph (differentiability implies continuity). -IMP ;) :)
Answer : You use a slope field. Remember: the derivative of a function at a given point is the SLOPE of the original function there. For example, if f ' (3)=7, then the SLOPE of f at 3 is also 7. So you know that f(0)=1. Look at the value of f ' (0), and make s short line segment that crosses (0,1) with that slope. Follow that line and continue on with this technique using each value (1, 2, 3, and -1, -2, -3, etc). When you're done, connect the line segments to form a continuous graph (differentiability implies continuity). -IMP ;) :)
Question : I have a second order step response graph. It has overshoot, oscillates and settles to a value.
Is it possible to derive transfer function by looking at this graph?
E.g. How to measure damping ratio and natural frequency from a graph?
Or what is overshoot, settling time, and oscillation frequency in terms of natural frequency and damping ratio?
Answer : Sure. If it has overshoot, the damping ratio is between 0 and 1. http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/Ident1A14.gif http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/Ident1A15.gif Figure out the frequency of the response and apply the following eqn. http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/SysDyn2A4A.gif See link for more details .
Answer : Sure. If it has overshoot, the damping ratio is between 0 and 1. http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/Ident1A14.gif http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/Ident1A15.gif Figure out the frequency of the response and apply the following eqn. http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/SysDyn2A4A.gif See link for more details .