I suspect that "N=2k-1 where k=1, 2, ... " is simply a portion of the solution given by your book.iScience said:Homework Statement
my function: [itex]sin\frac{N\pi}{2}[/itex] , N = 1, 2, 3, ...
N = 1 ---> f(N) = 1
N = 2 ---> f(N) = 0
N = 3 ---> f(N) = -1
Homework Equations
The Attempt at a Solution
[itex]-\frac{1}{2}(-1)^N[/itex]
obviously it's wrong but just an 'attempt'
my book refers to the substitution N=2k-1 where k=1, 2, ...
but i don't understand how this returns the correct values.
any thoughts?
To plot a discrete function, you can use a scatter plot or a line plot. A scatter plot is useful when the function has a limited number of data points, while a line plot is better suited for functions with a large number of data points. Both types of plots can be easily created using software tools such as Excel or Python.
The best way to visualize a discrete function depends on the specific data and the information you want to convey. Some common methods include plots, histograms, and bar charts. It is important to choose a visualization that clearly represents the data and makes it easy for others to understand.
Choosing the right scale for a discrete function plot is crucial in accurately representing the data. The scale should be chosen based on the range of values in the data. For example, if the values range from 0 to 100, a scale of 1 unit per tick mark would be appropriate. It is also important to consider the precision of the data and choose a scale that highlights any patterns or trends in the data.
Yes, using different colors or symbols can be a helpful way to differentiate between data points in a discrete function plot. This is especially useful when there are multiple data sets being plotted on the same graph. It is important to use a color or symbol key to explain the meaning of each color or symbol used.
The x-axis of a discrete function plot should represent the input values of the function, while the y-axis should represent the output values. It is important to include labels that clearly indicate what each axis represents and include units of measurement if applicable. You can also include a title for the plot that describes the function being represented.