How can you determine which variable is dependent and which variable is independent

MrBillDoesMath!

 The dependent variable depends on another variable for its value. For example, if  y = 2x,  setting x = 1 forces y= 2.; setting x = 10, forces y =20.  There are no other possibilities for y once x ids chosen. So y is the dependent variable and x is the independent one. You can pick values for the independent variable (x) but no so for the dependent one.

MrB

This is actually quite a deep-going question. To truly determine which variables (in an experiment, or in an observation of nature) depend of other variables is sometime very difficult and laborious. In math this may be easier. See detail below.

In pure mathematics, where variables do not necessarily carry a physical meaning, the determination is a matter of definition. A variable is defined to be dependent on another variable, for instance, y depends on x via the specific function, y = 10x + 10. The key is: this is given. Otherwise (if it were not given), suppose I gave you an equation a+b=10 and not told you which is the dependent and which the independent variable. You could think of each being either: a=10-b and b=10-a. Without this being defined, there is no clear way to determine dependency.  

In science, on the other hand, the determination is made based on experimental design and based on certain plausible assumptions about natural dependencies. For example, if you design an experiment to measure some physical quantity, such a height of an individual, you can look at the that as a variable dependent on other variables, such as age, ie., what is the average height of a person given their particular age (say, 0, 1, 2,..., 18 years of age). It would be more of a stretch to measure the age as dependent variable of height.

I hope these thoughts are helpful.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

pla·gia·rism

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noun

the practice of taking someone else's work or ideas and passing them off as one's own.

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