E ASSESSMENT
Directions: Read the excerpts of the speeches below and answer the questions
follow.
A.
We won't suddenly agree on everything now that the cloud of crisis
passed. But we shouldn't hold back on places where we do agree, just bec
we don't think it's good politics. Or just because the extremes in our parties
like compromise. I'll look for willing partners from either party to get imp
work done. There's no good reason why we can't govem responsibly,
lurching from manufactured crisis to manufactured crisis. Because th
governing - it's just hurting the people we were sent here to serve
1. How does President Obama define the word "govern"?
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This is the concept of a piecewise function. for your function, you have



the second halves tell you the interval in which the left equation is graphed in. they are defined as such. they are there because whoever made the notes/question/whatever the picture is literally defined the function to be like that. the graph ends up looking like that.

means between  (inclusive)  and  (inclusive). 

means between  (exclusive)  and  (inclusive). 

for example, between -2 and 3 (inclusive), the function graph will have the equation , which is a line with y-intercept of 1. then, between 3 (exclusive) and 7 (inclusive), the function graph will have equation  , which is a parabola with vertex at (5,0).

as for why those two definitions of the function can mean the same thing:



and 



and have the same value at  , so it does not matter which piece gets the "equal to." notice how they changed which piece gets the  (less than or equal to).

if both pieces were to be defined at  , then the function would not be a function (because it would technically have one domain element mapping to two range elements). so we have to leave one piece that doesn't include  .


i have attached another example of a piecewise function.

note that piecewise functions are not just limited to straight lines and parabolas; they can be anything that you can graph.