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Question 165497: This is probably so basic but it's been a VERY long time and it just doesn't make sense to me. Please help! Thanks
1. Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.
a. f(x) = x + 5
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! here's the definition of function.
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A function is an equation (this is where most definitions use one of the words given above) if any x that can be plugged into the equation will yield exactly one y out of the equation.
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looking at each of your selections will help to determine if they are functions or not.
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a. f(x) = x + 5
i would say yes.
for every value of x, there can only be one value of f(x).
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b. f(x) = 3 if x>2 otherwise f(x) = -2
i would say yes again.
for every value of x, there can only be one value of f(x).
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c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
i think no.
it looks like at first glance, that this would not be a function since it looks like there can be more than one value of f(x) for a value of x.
the first part says
f(x) = 7 if x > 0.
that's one value of f(x) for every value of x > 0.
the second part says
f(x) = -7 if x < 0.
again ok. that's one value of f(x) for every value of x < 0.
the third part says
f(x) = +/- 7 if x = 0.
here's where it falls down.
that's 2 values of f(x) when x = 0.
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definition says a and b are function, c is not.
check out paul's online notes for a review of the subject if you have time.
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http://tutorial.math.lamar.edu/classes/alg/functiondefn.aspx#Fcns_Defn_Ex2
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