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Numerade Educator

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Problem 9 Medium Difficulty

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

Answer

All members of the family of linear functions $f(x)=c-x$ have graphs that are lines with slope $-1 .$ The $y$ -intercept is $c$.

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Video Transcript

Okay. This function here actually represents a whole family of functions. And let's figure out their common feature. So what if I rewrite it in a form that's a little bit more familiar to us? I'm going to write it in slope intercept form, which is y equals MX plus B. So I'm going to rename F of X says why? And then I'm going to rearrange the terms on the right side of the equation. So now that we have it in that form, we can see that the slope is negative one and the Y intercept is see. So that's an indication that we have a variety of different Y intercepts, but all the lines will have a slope of negative one. So that's what they have in common. This slope. Let's sketch several lines that have a slow, good negative one, so one of them could be y equals negative one x plus zero just Weichel is the opposite of X. That would look something like this. Why intercepted zero slope of negative one another. One could be y equals the opposite of X plus one. Why intercept of one and a slope of negative one thes would be parallel. Another one could be y equals the opposite of X minus one, which has a Y intercept of negative one. Also a slope of negative one. So all three of those are parallel.