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Question

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abb0t · Answer

One question per post.

e.mccormick · Answer

Actually abb0t, it is one question in two parts.  Why not look at it before biting them.

e.mccormick · Answer

cassandralombardi, do you know what evaluate $f(0)$ means?

abb0t · Answer

I am just going by the rules stated here: http://openstudy.com/code-of-conduct and here: http://openstudy.com/terms-and-conditions Also, I am not Biting them! I'm not a cannibal. Plus, I am not even within close range to the user. They are probably many miles away from me.

e.mccormick · Answer

Actually, there is nothing in there about doing a single question per post.  It is just the multiple questions limits medals so it is commonly accepted that it is better to ask one question per post.

e.mccormick · Answer

Yes.  So put 0 in, use the proper part of the piecewise function, and get the answer.

e.mccormick · Answer

As for the graphing part, well, you graph both pieces, but make sure to denote what they include.  So that $x\le 1$ needs to be inclusive at that point and the $x > 1$ is not.

e.mccormick · Answer

No, it only goes into the part that says it is valid for 0.

e.mccormick · Answer

It might be clearer when I replace the , with if.

$f(x)\begin{cases}
x^2 & \text{ if } x\le 1 \ 
2x+1 & \text{ if } x> 1 
\end{cases}$

That is what the , means.  Piecewise functions mean "use this, if it is this."

e.mccormick · Answer

And yes, that revised version is correct for evaluating it.  So what does that give you as an answer for $f(0)$?

e.mccormick · Answer

Well, what is $0^2$?  I mean, $a^2=a\cdot a $ so $0^2=0\cdot 0$ so what is that in the end?

e.mccormick · Answer

Yep.  So that is what it evaluates to.

e.mccormick · Answer

Yes.

e.mccormick · Answer

Well, you should know how to grah a parabola and a line, which is what the parts are.  But, you only graph each for where it says it is valid.  The parabola part says $x\le 1$ so your graph must show that.  The line says $x > 1$ so it must also show that.

Know how to show something is included or excluded on a graph?  Dot vs circle mean anything?

e.mccormick · Answer

Hmmm.... that line does not seem to have the right starting point and the parabola starts and stops in the wrong place.  So you are beginning to get the idea, but need to work on it a bit.

Remember, because the $x^2$ is valid for everything up to 1, it will keep going on the left and end at x=1 as the right most point.  The line starts for everything above x=1, so you can use x=1 as the start.  It just needs an open circle there, which the graphing program may not show.  And check what you have in there for the calculation.  2x+1 at 1 would be 3.  So it needs an open circle at 3.

e.mccormick · Answer

Yah, that looks more like mine: https://www.desmos.com/calculator/edwmnyjjjd