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The graph of f Is glven_ Use the graphcomoucequantitles asked for If a = (If an answer does not exlst; enter DNE:}...

Question

The graph of f Is glven_ Use the graphcomoucequantitles asked for If a = (If an answer does not exlst; enter DNE:}

The graph of f Is glven_ Use the graph comouce quantitles asked for If a = (If an answer does not exlst; enter DNE:}



Answers

Refer to the function $F$ in the graph shown. $U$ se the graph to determine whether $F^{\prime}(x)$ exists at each indicated value of $x$. $$ x=a $$

Okay, so here it wants us toe figure out if it's a function. And so the first thing we're going to do is do the vertical line test. So over here I drew this blue line, and the bird clientes just means you drag it. And I'm seeing some problems here, right? It's only supposed to at once, but I see even, like, right here, it hits 1234 times, Which means this is not gonna be a function, right. I said, if it is, you find f of three. Well, since it's not, we don't need to find out of three. So just do the vertical line test. You'll see it crosses and multiple spots, so therefore, this is not a function.

Okay, so this problem gives us this funky looking graph over here. Um, and it wants us to first find if it's a function, and if it is, then you find f of three. So to figure out some things that function, that means that has won out part for every input. So you're going to go ahead and do the vertical line test. So as I'm dragging this along, I say, OK, black and blue are only hitting in one spot until I get about here. Because if you see, they're kind of like overlapping in this whole section there. Which means if I plug in that negative one, I could get out anything along that line. So that's going to give you multiple spot. So this is not going to be a function, which means you don't need to find f of three

Okay, So here, um, we have this, like w looking graph. And so the first thing we need to figure out is if it's a function, and so that means it needs to be oneto one right one output for every input. And so that means we can use the vertical line test. I'm gonna go ahead and take this vertical line. I dont be dragging it. I'm looking so that black and blue only meet once. And if I'm looking here, it's looking pretty good. And so since I was able to go through the whole thing with it on Lee hitting once at a time, that means that yes, this is a function. So then to find f of three, we that's just where X is three. And then we need to say what? Why is right? And so we can't 123 and my pictures not super exact. Um, it's supposed to go up a little faster or something like that. Um and so there I'm thinking it's like maybe about negative 1/2 or so right, So negative, half ish. It doesn't really give us any. I'm indicators to make it exact. So I'd say it's negative. Half or so, but


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