A question on plotting functions on a graph

In summary, the conversation discusses the definition of a function and whether or not a line drawn parallel to the y-axis can be considered a function. The speaker questions how it can be considered a function if there are multiple outputs for each input. The responder explains that the concept of a function has evolved over time and that in some applications, multivalued functions are used. However, the current definition of a function is single valued.
  • #1
#neutrino
51
2
when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as
" if each line parallel to the y- axis and which passes through a point in the domain intersects the graph at only one point then our function is single valued " my point is since it is a line drawn parallel to the y- axis for each input there will be several outputs ,therefore how come it is a function at all?
 
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  • #2
It is not function. It is just a line.
 
  • #3
#neutrino said:
when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as
" if each line parallel to the y- axis and which passes through a point in the domain intersects the graph at only one point then our function is single valued " my point is since it is a line drawn parallel to the y- axis for each input there will be several outputs ,therefore how come it is a function at all?
It's nothing more than a question of terminology.
Currently a function is defined as single valued. In certain applications one uses the concept multivalued functions (complex logarithm for example).

Apparently our current definition of function has changed with time.

From Wikipedia:
Wikipedia said:
The practice of allowing function in mathematics to mean also multivalued function dropped out of usage at some point in the first half of the twentieth century. Some evolution can be seen in different editions of A Course of Pure Mathematics by G. H. Hardy, for example.
It probably persisted longest in the theory of special functions, for its occasional convenience.
 

1. How do I plot a function on a graph?

To plot a function on a graph, you will need to determine the x and y values for different points on the graph. Then, plot these points on the graph and connect them with a smooth curve to represent the function. You can also use a graphing calculator or software to plot the function automatically.

2. What is the importance of plotting functions on a graph?

Plotting functions on a graph allows you to visualize the relationship between the variables in the function. It can help you identify patterns, zeros, and maximum or minimum points of the function. This can be useful in understanding the behavior of the function and making predictions.

3. How do I determine the domain and range of a plotted function?

The domain of a function is the set of all possible x-values for which the function is defined. To determine the domain of a plotted function, look at the x-axis and identify the range of values that the function is defined for. The range of a function is the set of all possible y-values that the function can take. To determine the range of a plotted function, look at the y-axis and identify the range of values that the function can take.

4. What are the different types of graphs used to plot functions?

The most common types of graphs used to plot functions are line graphs, bar graphs, and scatter plots. Line graphs are used to show the relationship between two continuous variables, while bar graphs are used to compare discrete variables. Scatter plots are used to show the relationship between two variables and identify any patterns or trends.

5. Can I use a graphing calculator or software to plot complex functions?

Yes, graphing calculators and software can plot complex functions with ease. They have built-in functions and features that allow you to plot a variety of functions, including trigonometric, exponential, and logarithmic functions. They also allow you to adjust the scale and view of the graph to better understand the behavior of the function.

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