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Question 999461: ok, so i'm in algebra one, and i have a test tommorow on our unit. one thing I don't get is domain and range. it shows an oval, and three numbers inside. i get the first and last one, but not the middle one. I don't know how to make a piecewise function with the {{}} thing so i'll put it as 2 layers. the piecewise function that i need help on is:
f(x)=3x+11 -5<=x<=-2
-x/2+5 -2
sorry for bad grammar i rushed through this! :)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! one thing I don't get is domain and range. it shows an oval, and three numbers inside. i get the first and last one, but not the middle one. I don't know how to make a piecewise function with the {{}} thing so i'll put it as 2 layers. the piecewise function that i need help on is:
f(x) = 3x+11 when -5<=x<=-2
f(x) =-x/2+5 when -2 < x <=4
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Domain
This says the Domain (values of x) is "All Real numbers greater
than or equal to -5 and less than of equal to 4".
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Range
The range is the set of values "y" takes when the domain values are applied.
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y = 3x+11 has values between f(-5) and f(-2)
f(-5) = (3(-5)+11) = -4
f(-2) = (3(-2)+11) = 5
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y = (-1/2)x+5 has values from f(2) and f(4)
f(2) = (-1/2)(2)+5 = 4
f(4) = (-1/2)(4)+5 = 3
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So, what is the range?
The lowest value is f(-5) = -4
The highest value is f(-2) = 5
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So, the Range is "All Real Numbers from -4 to 5".
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You will see the Domain and the Range if you graph
each of the pieces of the function on its own Domain.
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Cheers,
Stan H.
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