 So, I will not talk about standard parabolic functions, the most standard of it is y equal to x square, again you should immediately stop me, say sir please write domain and the function, first of all I am not sure whether it is actually a function, I should call it as a relation, so you should say sir stop using the word F, you should call it as a relation, you should say I get it as f of x, are you sure that this is a function, so from my experience I humbly say yes I am sure, but from your side you should always challenge the fact how are you using the word F, F for functions again do not go to some other trajectory altogether, so here F should be used only when you know it is a function, else use R with a single line, is that fine, but since I know I have been teaching this for 11 years now it is a function, does not mean for that, I will never give you wrong information on this, now assuming it is a function, can we see the graph for it, I am sure you would have seen this empty number of times in the chapter quadratic equations, and even by closing your eyes you can actually draw the graph for this, yes or no, by the way couple of things which I want to know, what does this arrow signify, goes up and up never stops, now if it never stops how much is the span of this function along x axis, I have only mentioned it, so you should say sir you have only stated this span is going to be R, but if I say this is not R, but this is only a chart, there is some intervals that I would be denoting in our maths, so I will be giving you just a quick idea about that, this is also a part of the bridge because these small small things you should be doing, intervals are basically from their subsets of the real numbers from where my function can be spanning, for example if I see my function only spans between minus one to one, so I will not draw this part of the function, so I will not draw an arrow, it will only stop like this, then that interval would be called as minus one to one closed, minus one and one are included in your, understood whats the good thing, arpita, arpita you understand the meaning of the word closed means I include minus one and one point in my domains, then what is the meaning of open then, this is called closed, open means, what does it mean, it means not they themselves at the corner position, yes I am repeating this again, when you say open interval minus one to one, everything is point zero, minus point nine nine nine, that is minus one and one they are, are you getting it, so that is it, don't get confused with this, what is the difference between these three expressions, this is a set, this will only contain two elements, what are they, minus one and one, this contains all the set of points which lie between minus one and one, all the x value which lie between minus one and one on the real number line, including minus one and one itself, when you write this what does it mean, all the set of points between minus one and one are that then minus one and one themselves, so for this if I have to plot this graph, dear students please note I have to put a whole like this, what does this whole signify, that exactly at one this value here is missing, it is just ending before one, now how before, it is a matter of limits, that is a concept in calculus, so how before somewhere point nine nine nine nine nine nine, how much nine you want to add it, it is not attaining one, that is what I want to see over here, here also this whole signifies the same thing, it is just starting after minus one, are you getting this point, so if I write this minus one to one and I ask you, if I ask you what is the domain of this function, one to one set interval that is the domain of the function, I just know I am going to talk about the entire real number, so I have been raising this, I am putting the entire real number, so this graph is now extended in both the directions like this, now the next question is what is the range of this function, what is the range of this function, for domain look at the span of the function along x axis, for domain look at the span of the function along y axis, domain, range, domain, range, understood, so domain you said all real numbers, I agree with you, what about range, this is not the range by the way, this is what, its range is actually, I will write it as a short form like this, r f equals r f to signify range of a function, d f to domain of a function, don't ask me what is r f, so r f is going to be all positive real numbers, can I write it like this, hope you are aware of the symbols which we use r and w, z, what is z used for, integers, i is also used for integers, i plus means positive integers, r plus means positive real numbers, is that fine, what is this minimum, are you going to calculate something, in case of a parabola, is that fine, okay, it is called the vertex of the parabola, again you have sections coming up in class 11 for you, I will speak in detail about this, okay, now I have certain questions for you to answer, so we just now saw the graph of y is equal to x square and it was like this, assuming its domain is all real numbers and cotomain is also all real numbers, I would like, if I have to plot this graph, how would it look like, what do you think Shishant, it would become somewhat, is this correct, okay so we have another answer, it will shoot down, Shishant is outrightly rejecting your claim, what do you think, Shishant is correct, just because it comes from that one, correct, how do you think, I don't think so, right now, especially in maths class, I love challenges, please challenge somebody's answer, if you accept the answer, tell me why it is correct, if you are not, tell me why it is not correct, Ananya, you can't think, okay, at this point at least this guy is saying that the vertex will come, okay, so initially when it, correct, the vertex position initially was suggested, he is saying that when x is, so when x is 1 is y is 0, at least he is correct with respect to that, yes sir, but that doesn't mean the answer that he is giving is completely correct, only that one point satisfied it, may not be the other case, now Foreman sense says that, if I had, in the previous graph I had to put x value also as 1 or minus 1, but to get the same, the second graph as 1, I have to put either my x as 0 or my x as 2, so to get a value of y is 1, either I have to put x as 0 or y as 2, so 0 or x as 2, right, this is a value of y is equal to 1, right, so what he said is absolutely correct, the blue one would be the graph of y is equal to x minus 1 the whole square, now no points for guessing the graph of y equal to, this is the y equal to x plus 1 the whole square, how would be the graph of this, now the same logic, now your graph will actually which the ratio I choose there, the graph will shift on this side, that means the vertex will now come at minus 1, 0, understand, now here comes the rule for you, what is the rule, basically says in any function, when I say any function means any function, not only with a parabola, not only for a parabola, but even for a line, even for a trigonometric function, even for a logarithmic function, even for an exponential function, even for any special function, whatever function you can think of in this word, the rule is this rule, it says that if you replace your x with x plus h, h being a positive quantity, then the graph will shift h units to the left, h units to the left, that's what happened over here, when I replace x with x plus 1, my graph shifted 1 units to the left position, so from your side left position, if you replace your x with x minus h, again h being a positive quantity, your graph will shift h units to the right, your graph will shift h units to the right, is this rule understood, and you can actually apply it to any graph, let's say can I move to the next slide, let's say you know the graph of y is equal to x, yes everybody knows it, how does it look like, it looks like a straight line like this, correct, I will signify it, it indifferently keeps on going, the moment I say hey draw the graph of x minus 4, won't it appear like this point, and this point the shift will be of, that's why it ends, as you can see minus 4 is your y into 7, so my point here is that any function in the world, that rule is going to be holding 2, understood, but let's return back to the same graph, now my question is 5 minus 4, x square equals 1, I mean the word h, this graph, original graph black mark will move where, 1 unit half, 1 unit x will move, okay Krishna, Krishna is not part of the world today, so shares is everything, saying that the same graph will go 1 unit up, is it true, is it correct, why, because if you see this is another way, we know that x plus 1, the graph of x square plus 1 is the graph of y equal to x square shifted 1, is correct because if you put, initially when you have, but now when your x is 0, y will now become a 1, so for the same x, y will now assume a value as 1, so it's vertex will shift to which position, 0 comma 1, correct, so now the graph, something like this hanging in the air, okay, this point we have for, understood, what will happen if I ask you to plot the graph of 1 equal to x square, can I say that, can I append this rule and say that, if you replace, what's the quantity, the graph shifts the graph sideways, now understood, can I combine these two rules and give you a problem, will you be able to solve it, okay, sure, so this is the handout which I am going to, anyways give it to you, okay.