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For the function f(t) whose graph appears above; find the value of f(2). undefinednone of the choices...

Question

For the function f(t) whose graph appears above; find the value of f(2). undefinednone of the choices

For the function f(t) whose graph appears above; find the value of f(2). undefined none of the choices



Answers

For the function $f$ whose graph is shown to the right, find all $x$ -values for which $f(x) \leq 0.$

This example gets just a graft to look at and ask us to look in a variety of values and determine the domain and range of this graph. So the first thing we're looking at a specific X values and why values Remember, with function notation f of X notation, we could provide specific inputs, which would be X values of a graph, and be asked to find output. So this question would ask us if the X value on the X axis if the X value was one. What is the corresponding live value of that point? So, in other words, the point on the graph is one comma something, and I want to know what that why value is that goes with the X value of war. So if I look at the one on the X axis, the point that corresponds with it is down here and that is that the 0.1 common negative, too. So therefore, when f of access an input of 1/2 of one, the output is negative two. Or, in other words, one common negative two is the point on the graph with an input of one. Okay, then recon specifically look at the domain of the function. So what? The domain. We can look at the X value. So we're focusing specifically left to right, and we're noticing what are the bounds of the function of the X axis? So what is the smallest X value and what is the largest X value on the ground? So over here on the left hand side, this is a left. Most point that X value is that negative 22 boxes elect of the origin or 00 and the her. This right point is this top point, and that has an X value of 345 So therefore, my domain is between negative two and five. We can write this in a couple different ways. We can write this an interval notation that we used brackets because we have closed circles and the two billion there included, and we could give our smallest value and our largest value. This is saying that between negative two and five is all of my data, including negative to a negative five. Another way we could write this is we could say all the X values such that that's what the vertical line means the X has to be between negative two and positive five, and to use those words between, we typically use these inequalities. Sometimes to say the exits reader than or equal to native to the axe has to be smaller than or equal to five. So the X is in between those two values. It could be any numbers. Whole numbers got symbols, etcetera that fall between negative two and five. So these are the two notations we can use to write. They'll meet the domain is either between they get us to and five using the interval notation. Or we could say the exact same way and they all of the X values such that next meets this condition where it's between negative two and back. Okay, The other thing we can look at is given the y values. We can look at corresponding X values, So using function notation What that looks like is that you would be given the f of X value in this case were given an f of X value of two, and you're asked to find the X value that corresponds with that wide value. So this is telling you that the Y value of a point is to, and they want to know that expertly. That corresponds with that point. So now we look on the lie axes. That too we could track or is obviously to find the point that has that Y values and the coordinates of this point. Here are four comma two to the X value than the white value to enable a point. So when the Y value is two or the F of X value is to the corresponding, next value is four. That's how we would answer that question or another word. The 0.4 comma two with on the ground. So they gave us the y coordinate. You're trying to find the X coordinate of that and then lastly, along with y values, we can think about range, Remember, ranges all the possible. Why values so with why values We'd be looking vertically instead of horizontally, and we want to look at the lowest point to the highest point on a graph. The lowest point on a graph is down here again in this coordinate point member looking at why values? It was negative two for the X values, but for the y values that point of that negative three. That's the lowest. Why about you? I have the highest point that I have when my graph is up here again and again. If I look at my y axis, that's a lie. Value of four. So the range of my data, if I think about interval notation, is between negative three and four again, we're including those values with brackets instead of parentheses to know that the negative 34 also included on the graph. And then, if we want to use our other notation, we could say that it's all the Y values, such that. So why is between native three and four and again for between? We use those less inter equal to symbols. So all the y value such that why is bigger than negative three. But why is smaller than or equal to four? So here's the answers to our four questions that we were asked in relation to this craft

So this is a not for a good drawing of the graph in your book, but it will serve our purpose. We have four things we need to answer about this graph. The first is what f one is. So this is the value of the function of X equals one. So if we go to the graph and we go over to X equals one, we see that corresponds to the ordered pair one negative one, which means the value of f of one is negative. One domain is all of the X values on my graph. So I'm going to be looking here. This is the lowest I go on the X. This is the highest. I go for X. So I'm looking at the values in between here and here. So X has to be bigger than negative for, but it can be equal, and X has to be smaller than are equal to three. So that's going to be my domain. Part. C asks for where the function equals to the exciting that gives you that. So I go up to two on the why access and I read over. It's easier to see in your book. It's actually crossing right here at negative three. So that ordered Paris negative 32 So the X that makes this true for the function is negative. Three. And then finally, for the range, we're going to do the same as we did with the domain ranges on my possible. Why values? So the highest my y goes is at five. The lowest my y goes. Is that negative too? So why has to be between negative two and five, but it can be equal to both of those.

This is a multi step problem that asked us to look a different aspects of the graph of the function. The one thing we can look at with grasses we can evaluate specific. Remember, with function notation in the parentheses we put the input value or the X value that were interested in so f of one would indicate that we're looking for the one on the X axis, and we want to know the Y value of the coordinate point that correspond with that X value. So in this case, if we traveled vertically from the 0.1 on the X axis, we get to this 0.1 comma three. So therefore, when the input value is one, the output value is three the y value that corresponds. Excellent. US three. I'm thinking of it in terms of coordinate point and access for the y value that corresponded with one. Any answer for that point is one comment. Another thing with X values that were often after finding the domain so specifically with the domain of a function. We're looking at all the possible X values that the graph covers. But I want to know I'm looking left to right. Is that the direction that are X axis travels? I want to know the possible X values that the graph covers. So I look at my for the left point, which would be here and my furthest right point down here. Now I'm gonna look at the X values that correspond to those. So the furthest left point is negative one on the X axis and this furthest right point is that four on the excess. Now we have two different ways. You can write the deleting the first way is using interval notation. So I can note that the domain is between one negative one and four, and this is how we would write it. So the bracket instead of parentheses, these brackets indicate that those two values are included. So since we have closed circles or closed bosses are endpoints of our function, we know that negative one and four included values, and then the negative one in the four is the lower bound or the smallest value, and the four is the highest value. So this notation means all the numbers that are in between negative one and four, including those two numbers the second way we could write the domain IHS saying that the domain is all of the values X such that that's what the vertical line means. Exes between negative one and four and for between we often right domain is compound inequalities. This says the X is bigger than or equal to native one, but it's smaller than or equal to four. So all the X values such that X is between negative one and four. So as long as that condition is true, it's gonna be part of the dummies. Okay, The other thing we can focus on with functions graphically is the y values. So thinking about the Y values we could be given the f of X value, which remember, is the same thing, is just saying the y value and we could be asked to determine the xlu that corresponds with it. Took the Y value. The f of X value is too. I'm now look for two on the lie access this vertical access, and I'm gonna look horizontally this time to see the X coordinate that matches with that point. So the point that has a Y value of two is that looks like three on the X axis of three comma two to the 0.3 comma two means that when the output value is to the input value is three. And that's what this question is asking for. It gives us the output value of two. So the input value that would get us there is the input. And then again, thinking about the range. Now I wanna look vertically because I'm looking at the line access of values. So again, I'm gonna look at these two red points I have label because that's now the lowest point also in the highest point. So our lowest point down here corresponds with the Y value of one, and our highest points up here corresponds with a Y value of four. So therefore, our ranges between one and four. This is our interval notation using our brackets. Or now that we're talking about, why values we could say all y values such that the why is between using this compound inequality notation between one and four and I'm using equal to symbols because it could be equal toe one and four. And again, this is all of the Y values as long as they fit that condition. So here's our solution to our question because we identified the Y Value and X is one. We've noted the domain. We have a couple of different ways we could write it. We've been given a Y value and found the corresponding X value, and we've written the range in a couple different ways, and that was all using the graph that was provided to us.

So here is a not very good drawing of the graph that's in your textbook, but it will serve our purposes for explanation. So four things I need to answer about this graph the first is to tell me the value of the function when X equals one. So if I go over to X equals one, I'm looking for the point on the graph, which is right there. And that is at the 0.11 So f of one equals one. I then need the domain, which is all the possible X values. So my exes can go is low as negative three and my exes can go is high as five. So my domain is all the exes between and including negative three and five. I know those air included because these air closed circles, so that means they are part of the solution. Third step is defined the X values where the function equals two. So if I go up to two on the y axis and I read across to my graph, I can see that my graph ash, this one has drawn a little badly. It should be over here that if you look in your book. Your graph crosses has a Y value of two when x is negative one. So I know that my ex value here equals negative one. Finally, I need to do the range in the range of going to do the same as the domain. I'm gonna look for the highest point on why and the lowest point on why so again, those air inclusive because the dots are closed. So my no, my range will be a small zero and can be as large. That's a why and could be as large as four. So there are your answer.


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