Matlab Graphing With Exponential Function

What are exponential functions in MatLab?

In MATLAB exponential function-Y = exp(X)Y = exp(X) returns the exponential e^x for each element in array X. For complex elements z = x + iy, it returns the complex exponentialez=ex(cosy+isiny) .for example-exp(2)= 7.3891For Matrix exponentialy=exp(m)for exampleA = [1 1 0; 0 0 2; 0 0 -1];
exp(A)

ans =

2.7183 2.7183 1.0000
1.0000 1.0000 7.3891
1.0000 1.0000 0.3679

Is it possible to describe the graph of an exponential function like y=e^x using a polynomial function?

Yes. Just do what your computer does. Common computer programs that draw your graphs of e^x call standard library functions to obtain their values for e^x. These standard functions approximate the value of e^x with algorithms that use polynomial approximations to the exponential function. You could borrow such an algorithm from public source code for the exponential function if necessary. But, it is simpler to allow the compiler or interpreter to call the code for you. It is likely that every graph of e^x and every value for e^x that you have used, or will use, is the result of a polynomial approximation. If so, for you, every description of the graph of an exponential function is already a polynomial function — there is no practical alternative. To be clear, the polynomial that approximates e^x at one point in its domain is generally not the same as the polynomial that approximates e^x at another point in its domain.

How do I graph exponential functions in LaTeX without PGFPlots?

Have you heard of SageTex? It lets you use Sage functionality directly in your TeX. Using SageTeX - Sage Tutorial v7.6It works well and it’s really neat, but I’ve found it to be a bit of a pain to install. It is probably installed by default on the Sage math cloud: Collaborative Calculation in the CloudYou could also create your document in a Sage worksheet (which supports LaTeX).

How do I build an exponential equation in MATLAB Simulink?

More clear answer can be given if you give the equation.See the link below, you can use the math function block.Perform mathematical function - Simulink

How do I graph functions in math?

It is a very general question and hope that the following guidelines help you.Find the domain of the function, will be useful when we find the vertical asymptote and critical points.Find the [math]x[/math]- and [math]y[/math]-intercepts, set [math]y=0[/math] and [math]x=0[/math], respectively.See whether the function is even, odd nor neither, odd function will have a [math]y[/math]-intercept at the origin.Find the vertical, horizontal and slant asymptotesFind the intervals where the function is increasing and decreasingFind the local minima, maximaFind the intervals where the function is concave upward and concave downward. Find also the point of inflection if it has.Example (from Nipissing University, cont’d)[math]f(x)=\frac{x^2+5x+4}{x^2}[/math]Domain: [math]\{x|x\neq0\}[/math][math]x[/math]- and [math]y[/math]-intercepts: [math]y=0\implies x=-1[/math] or [math]x=-4[/math]; undefined at [math]x=0\implies[/math] no [math]y[/math]-interceptSymmetry: [math]f(-x)=f(x)\implies[/math] odd function, note that [math]f(0)[/math] is undefinedAsymptotes: vertical ([math]x=0[/math] as [math]\lim_{x\to0^-}f(x)=\infty=\lim_{x\to0^+}f(x)[/math]) ; horizontal ([math]y=1[/math] as [math]\lim_{x\to-\infty}f(x)=1=\lim_{x\to+\infty}f(x)[/math])Monotonicity: increasing [math](-8/5,0)[/math]; decreasing [math](-\infty,-8/5)[/math] and [math](0,\infty)[/math]Local minima and maxima: [math](-8/5,-9/16)[/math]Concavity and point of inflection: concave upward [math](-12/5,0)[/math] and [math](0,\infty)[/math]; concave downward [math](-\infty,-12/5)[/math]; point of inflection [math](-12/5,-7/18)[/math]The plot looks like this plot (x^2+5x+4)/x^2 in [-10,10]

What is the difference between Linear and exponential functions?

“Linear function” can mean a couple of things. But in the context of high-school-level algebra, the basic ideas are like this:A linear function is one that is changing at a constant rate as [math]x[/math] changes.An exponential function is one that changes at a rate that's always proportional to the value of the function. A simple example is population growth for a very simple kind of organism, like bacteria. The larger the population is, the more the population will increase. (This is also assuming that the population hasn't gotten too large for its habitat.)That might not seem so clear, but the difference between them might be easier to see if you look at the values of [math]f(0), f(1), f(2), f(3),[/math] and so on.First let's look at the general formulas:Linear: [math]f(x) = ax + b[/math]. (You'll probably often see it as [math]f(x) = mx + b[/math], but let's stick with [math]ax + b[/math] so we can see the parallels between these concepts more easily.)Exponential: [math]f(x) = ba^x[/math], where [math]a[/math] is a positive number other than [math]1[/math].When you look at the linear function and compare [math]f(0), f(1), f(2), f(3), \ldots[/math], you may notice that when you add [math]a[/math] to [math]f(0)[/math] you get [math]f(1)[/math]. When you add [math]a[/math] to [math]f(1)[/math] you get [math]f(2)[/math]. When you add [math]a[/math] to [math]f(2)[/math] you get [math]f(3)[/math], and so on. Each time you increase [math]x[/math] by [math]1[/math], [math]f(x)[/math] gets [math]a[/math] added to it.(In this case, [math]f(0), f(1), f(2), f(3), \ldots[/math] form what we call an arithmetic sequence.)The exponential function has a related idea going on. When you multiply [math]f(0)[/math] by [math]a[/math] you get [math]f(1)[/math], and it goes on like that.(In this case, [math]f(0), f(1), f(2), f(3), \ldots[/math] form what we call a geometric sequence.)Another thing you might notice, from playing around with these different functions, is that in both cases, [math]b[/math] is the “starting” value. In other words, [math]f(0) = b[/math].

How do you linearize an exponential graph?

Linearizing an exponential graph can be achieved by dividing the curve into straight lines of very small finite lengths. Each of these line is a linearized version of the exponential graph.Also, first derivative of the equation that satisfies the exponential graph is one of the methods of linearization.

How do you plot the half-closed interval of a function in MATLAB?

Not necessary, there is no continuous interval in MATLAB.But if you insist on doing this,the follows could be referent:The code is like this:x=1:.01:2;
y=x.^3;
plot(x(1:end-1),y(1:end-1),'-',x(end),y(end),'o')
axis([0.5 2.5 0 9])