Adriana A.

asked • 02/03/16

Is this function a linear function? Why?

f(x) = √5x-15

Michael J.

Adriana, in order to get the best an accurate answer, be sure to use parentheses to make you expressions and equation clearer.  Order of operations is the most important concept you will ever learn in math.  Your function could have been interpreted as
 
f(x) = √(5x) - 15   --->  5x is under the square-root.
 
or
 
f(x) = (√5)x - 15   ---->  This would make it linear as Nathan mentioned.  The slope is √5.
 
or
 
f(x) = √(5x - 15)   ---->  Everything is under the square-root.
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02/04/16

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Michael J. answered • 02/03/16

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This function is not linear for several reasons.
 
Reason 1:  Linear functions do not have square-roots in them.
 
Reason 2:  Linear functions represent straight lines on a graph.  The function you have represents a curve.
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Kenneth S.

Nathan B's answer is the best one.  The problem is that the means of writing mathematical expressions in this platform aren't very good.  If just the square root of 5 (a constant, albeit irrational) is the coefficient of x (i.e. x is not under control of the square root symbol), then the equation IS LINEAR.
 
By the way, the horizontal part of the usual radical symbol is called the VINCULUM--it's a grouping symbol. Originally the square root of 2 would be written either as √(2) OR √ followed by 2 with a bar over it. 
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02/04/16

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