For linear functions where the slope is zero, the function

f(x) = b is called aconstant function.The textbook goes on to say that the function in question islinear.not

Why is the constant function not linear?

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- December 25th 2008, 10:09 AMmagentaritaConstant Function
For linear functions where the slope is zero, the function

f(x) = b is called a**constant function.**The textbook goes on to say that the function in question islinear.__not__

Why is the constant function not linear?

- December 25th 2008, 10:53 AMmasters
If your textbook says that the constant function f(x)=b is not linear, it shouldn't have left it at that. Otherwise, I would question the integrity of the whole book. I would define the constant function this way:

__Definition of Constant Function__

- Constant function is a linear function of the form
*y*=*b*, where*b*is a constant. - It is also written as
*f*(*x*) =*b*. - The graph of a constant function is a horizontal line.

Now, if by the strictest rule of a linear function being functions that have x as the input variable, and x is raised only to the first power, one might interpret f(x)=b as non-linear, since it is a polynomial function of degree 0. To me, this is a stretch (departure) from the difinition of the term "linear" (the graph of which is a straight line). - Constant function is a linear function of the form
- December 25th 2008, 12:05 PMmagentaritanicely done....
- December 26th 2008, 11:24 AMHallsofIvy
There are at least two different definitions of "linear" function. In basic algebra and pre-calculus, it is common to refer to any function having a straight line as graph, which can always be written y= mx+ b, as "linear". That would include m= 0, y= a constant.

In linear algebra, a linear transformation is a function satisfying f(ax+ by)= af(x)+ bf(y). For real numbers, that is of the form f(x)= mx with "constant part" 0. Of course, even in that case f(x)= 0 with both m and b equal to 0, would be "constant" linear function.

What was the title of this textbook, what course was it for, and**exactly**what did it say? - December 28th 2008, 08:07 AMmagentaritagreat....