![]() ![]() How to stretch a function in x-direction?Īgain, like moving, stretchig is more difficult: We have to replace every x by (Mind that it is again not the way you may think: Stretching does not mean multiplying by, but dividing byĭein Browser unterstützt den HTML-Canvas-Tag nicht. Transform the function by 2 in y-direction stretch : For example, lets stretch by Factor in y-direction. This is easy, again: Just multiply your whole function by the stretching factor. How to stretch a function in y-direction? | Apply the higher binomial formula with a= and b= Move the graph of by 2 in direction right : Here is another example involving the latter function. But if you want to go in the opposite direction, you replace x by. and mind the sign: If you want to go in x-direction, replace x by.If you want to move in x-direction, it is more difficult for two reasons: For example, lets move this Graph by units to the top.ĭein Browser unterstützt den HTML-Canvas-Tag nicht. Just add the transformation you want to to. In general, transformations in y-direction are easier than transformations in x-direction, see below. This depends on the direction you want to transoform. Vertical compressions and stretches of graph Vertical stretches of graphs. So, for any function when the output is multiplied by 1 it reflects across the xaxis. In general, g(x)1f(x), the graph of g is a reflection across the xaxis of the graph of f. Over and get you to G, which is exactly what we already got.How to transform the graph of a function? The graph of g(x)x 2 is a reflection of f(x)x 2 across the xaxis. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3. (Vertical reflection) f (x) - sine (x) Expansions and vertical compressions: To graph y af (x) If a> 1, the graph of y f. You were getting before, you now get the opposite value, and that would flip it Which set of transformations is needed to graph f(x) 2sin(x) + 3 from the parent sine funct. We could write this as Y is equal to four times F of X, or you could say Y is equal to four times the absolute value of X, and then we have a negative sign. If were to unflip G, so this thing right over here, this thing looks like four times F of X. If we were to unflip G, it would look like this. We even flip it over, if we were to unflip G, it would look like this. Reflection about the x-axis Reflection about the y-axis Vertical shifting or stretching Horizontal shifting or stretching Tell me if Im wrong, but I believe that in any function, you have to do the stretching or the shrinking before the shifting. "Hey, let's first stretch "or compress F." And say, alright, before ![]() And you could have done it the other way. So we could say that G of X is equal to, it's not negative absolute value of X, negative four times theĪbsolute value of X. Go from the green to G, you have to multiply this a reflection with respect to the x-axis, draw the resulting graph by. Times the negative value, so it's going even more negative, so what you can see, to The graph of cf(x) is the graph of f stretched vertically (from the x-axis). When X is equal to negative one, my green function gives me negative one, but G gives me negative four. For a given X, at least for X equals one, G is giving me somethingįour times the value that my green function is giving. ![]() It to be the same as G, we want it to be equal to negative four. On this green function, when X is equal to one, the function itself isĮqual to negative one, but we want it, if we want We appropriately stretch or squeeze this green function? So let's think about what's happening. So this is getting usĬloser to our definition of G of X. Whatever the absolute value of X would have gotten you before, you're now going to get the negative of the opposite of it. I'll call this, Y is equal to the negative absolute value of X. So this graph right over here, this would be the graph. So its just flipped over the X axis, so all the values for any given X, whatever Y you used to get, youre not getting the negative of that. So it's just flipped over the X axis, so all the values for any given X, whatever Y you used to get, you're not getting the negative of that. Its just exactly what F of X is, but flipped over the X axis. It's just exactly what F of X is, but flipped over the X axis. Let's actually, let's flip it first, so let's say that we have a function that looks like this. We could first try to flip F of X, and then try to stretch or compress it, or we could stretch or compress it first, and then try to flip it. So like always, pause this video and see if you can up yourself with the equation for G of X. Stressed or compressed, but it also is flipped over the X axis. What is the equation for G of X? So you can see F of X is equal to the absolute value of X here in blue, and then G of X, not only does it look G can be thought of as a stretched or compressed version of F of X is equal to ![]()
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