# Thread: Family of linear functions...

1. ## Family of linear functions...

"What do all members of the family of linear functions
f(x) = c - x
have in common?"

Answer in the back of the book is "The slope is -1"

I think I understand that, but...is there any particular reason it is written as f(x) = c - x instead of f(x) = c - mx? I'm guessing "m" is just implied or something, I don't know.

Also I don't really know what it means by "family" of linear functions.

2. ## Commutative Law

Hello.

f(x) = c - x is not written as f(x) = c - mx because the problem you are given has explicitly told you that the value of m would be 1 in your version of the equation.

I think that the larger problem here is that you might not be seeing this:

f(x) = c - x is the same as f(x) = -x + c because the commutative law allows you to rearrange the order of two items being added. Maybe your textbook wanted to save on the price of printing a '+' sign?

This is a line with a y-intercept value of c and a slope of -1 as the coefficient of x is -1.

A family of functions means that there is a bunch of functions that are all the same except they can differ by a constant. The c term in the equation is the constant. Graphically, this means that the functions behave the same way, they are just shifted up or down from one another.

Example:

j(x) = 3x + 3, k(x) = 3x - 2 belong to the same family of functions because they are the same function with just a different constant.

3. hurrr
I feel stupid now, I don't know why I didn't see the problem like that before. I guess the "family" term threw me off.

And thanks for the explanation of that too, because there is nothing about that in the book. Maybe it's something I should already know, but I don't.

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### what do all members of the family of linear functions c-x have in common

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