Use the graph of

Question

Use the graph of $f$ in the figure to find the following values or state that they do not exist.

$f\left(0\right)$

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. So refer to the graph of the function F to find F of zero. Awesome. So it appears our final answer that we're ultimately trying to solve for is we're trying to figure out what F of zero is awesome. So instead of it being F of X, where X is just an unknown variable, we're told that X is zero in this case. So we're trying to figure out what F of zero will give us and we can figure out fa zero by referring and using our graph that it or referring to our graph that is given to us by the prom itself. So as you can see looking at our graph, it appears to be a cosine graph because it doesn't cross through the origin point at 00. So you can see we have a lot of peaks and valleys. So it goes like little mountains and it goes up and down and it like makes a little zig zag pattern going through a graph and it's Y equals F FX and appears that we also have a hole at 0.3. So going on xae three and four, so 0.3 comma four and we have a hole and then we have a solid close interval at 31. Awesome. And appears our graph hits the axe or our vertical axis at 01. And I put a red dot to indicate where it hits on our vertical axis, I say yeah, or vertical axis. So with that in mind, let us read off our multiple choice answers to see what our final answer might be. A is zero, B is four C is one and D is fa zero does not exist. Awesome. So our first step to solve this problem is looking at at using our graph, we can determine that the graph of F the value of Y at X equals zero. So let's make a note here. So at X equals zero. So the value of Y at X equals zero is one. So that means without a doubt, our final answer is one which as you could see from our graph, like we said, so X first, so zero comma one is where it hits our vertical axe. So our final answer has to be one which looking at our multiple choice answers, the correct answer has to be letter C which is one and that's it. This problem is a very simple and easy one to solve for. So let us note that our final answer once again is c so as long as you have a strong understanding of the background theory to solve a problem like this, you need to understand that you need to be able to interpret a graph. And you also need to understand that if in this case, we, so referring to our graph, so the value of Y at X equals zero will be one. So as long as you could figure that out on your own, using your background theory and if anything I said doesn't make any sense, I would si would strongly suggest going back to reread that chapter in your textbook or to watch more videos on similar topics like this to get a stronger understanding. But once you do problems like this are very quick and easy to solve and that's it. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Use the graph of $f$ in the figure to find the following values or state that they do not exist. <IMAGE>
$f\left(0\right)$

Key Concepts

Function Evaluation

Graph Interpretation

Existence of Function Values

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