# Drawing Graphs with f(x): A Beginner's Guide

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• btb4198
In summary: The OP could do both: direct approximation using piecewise definition (using e.g. splines, as Nidum suggested) and a spectral approximation, and compare.
btb4198
How do I make a function that can draw this same graph ? Also, if i want to increase the frequency of the function, how do i do that ?
so I am thinking f(x) = sin(x) for -1<= f(x) =0.5; f(x) = e^(x)/10 for f(x)= <=1 ; f(x) = cos(x) for f(x) >=0.5
f(x) = -cos(x)
um... i do not think this is right.
help

Is this the graph of something you measured? Or is it the graph of something you simulated?

In either case, given a graph on a certain interval (say, a time interval) it is in general not possible to define a function in terms of elementary functions (such as polynomials, harmonics, exponentials, etc.) that replicates said graph, even when you allow for piecewise definition.

In a sense, the graph itself is the definition of the function you are looking for.

hi, so that is graph of an 12 Hole Ocarina playing the note e.
wait I can't make a function out of it ?

btb4198 said:
hi, so that is graph of an 12 Hole Ocarina playing the note e.
wait I can't make a function out of it ?
Nice. From your graph you can see that there is a harmonic in the background (probably its frequency corresponds to your "e"), but there is something else on top of it that reflects the fact that you are close to producing an "e", but you do not manage to do that with mathematical perfection.

Probably a spectral decomposition would show a peak at the "e" frequency, but in addition there will be some much smaller mini-peaks around it.

If you just want to draw the graph and manipulate it in a visual sense then use ordinate samples and a spline routine . Some spread sheets can do this but it is not difficult to write a program .

A method commonly used in engineering computation is to break down the curve of interest into a sequence of segments where each segment can be defined with a simple function .

Nidum said:
A method commonly used in engineering computation is to break down the curve of interest into a sequence of segments where each segment can be defined with a simple function .
I think that is what the OP was trying to do.

Because it appears this is the recording of a real musical instrument playing an "e", to me it would provide most insight to Fourier decompose the recording, keep as many modes as one likes and use these to reconstruct an approximation to the original signal.

The OP could do both: direct approximation using piecewise definition (using e.g. splines, as Nidum suggested) and a spectral approximation, and compare.

Krylov said:
I think that is what the OP was trying to do.

Because it appears this is the recording of a real musical instrument playing an "e", to me it would provide most insight to Fourier decompose the recording, keep as many modes as one likes and use these to reconstruct an approximation to the original signal.

The OP could do both: direct approximation using piecewise definition (using e.g. splines, as Nidum suggested) and a spectral approximation, and compare.

I was trying to do the
Krylov said:
Nice. From your graph you can see that there is a harmonic in the background (probably its frequency corresponds to your "e"), but there is something else on top of it that reflects the fact that you are close to producing an "e", but you do not manage to do that with mathematical perfection.

Probably a spectral decomposition would show a peak at the "e" frequency, but in addition there will be some much smaller mini-peaks around it.
sorry,
I am not understanding what you are saying here...

## 1. What is f(x) in the context of drawing graphs?

In mathematics, f(x) represents a function that maps an input value (x) to an output value (y). In the context of drawing graphs, f(x) refers to the equation or formula that determines the relationship between the x and y values and can be used to plot points on the graph.

## 2. How do I plot points on a graph using f(x)?

To plot points on a graph using f(x), first choose a range of values for x. Then, substitute each value of x into the equation for f(x) to calculate the corresponding y value. Plot these points on the graph and connect them with a line to create the graph of the function.

## 3. Can I use any equation for f(x) to draw a graph?

Yes, you can use any equation for f(x) to draw a graph. However, some equations may result in more complex or unusual graphs, while others may produce more common and recognizable shapes such as lines, parabolas, or circles. It is important to understand the properties of different types of equations to accurately plot points and interpret the resulting graph.

## 4. What are some common mistakes to avoid when drawing graphs with f(x)?

One common mistake is to plot incorrect points by substituting the wrong values of x into the equation for f(x). It is also important to accurately scale the axes of the graph and label them appropriately. Additionally, forgetting to include units on the axes or labeling them incorrectly can lead to confusion and errors.

## 5. How can I use f(x) to analyze and interpret a graph?

F(x) can be used to analyze and interpret a graph by examining its properties such as the slope, intercepts, and symmetry. These properties can provide information about the behavior of the function and its relationship to the input and output values. Additionally, comparing the graph of f(x) to other known functions can help identify patterns and make predictions about its behavior.

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