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# Reflecting & compressing functions

CCSS.Math:

## Video transcript

so we're told G of X is a transformation four of f of X the graph below shows f of X is a solid blue line so this is the graph of y is equal to f of X and G of X is a dotted red line so that's the graph of y is equal to G of X what is G of X in terms of f of X and they gave us some choices here and I encourage you pause the video and see if you can figure this out well there's a couple of ways that you could think about it one is if you just eyeball it it looks like if you flipped f of x over the x axis it looks a little bit like G of X but G of X looks like a version of that that's diminished a little bit so for example if you were to flip it perfectly over the x-axis you would get something you would get something that looks like and I'm just going to sketch it so if you just flip perfectly over the x-axis you would look you'd get something that looks like this and trying my best to eyeball it so it would look something something like this if you perfectly if you perfectly just flipped it over it would look something like that I might not get it perfectly right but that would be this right over here so let me be clear if this is y is equal to f of X then this line right over here that I just drew that be y is equal to negative f of X so because whatever f of X would give you just take the negative of it you're flipping over the x-axis and now G of X looks like a diminished version of that and if I were to just eyeball it it looks like it's roughly 1/3 of this so my initial guess and we can verify this a little bit is that this that this right over here is one-third the value of this so I would say it is so G of X is equal to one-third of negative f of X or negative one-third of f of X and that is not one of the choices which makes me extra cautious but let me just let me just emphasize why I like this choice because we've said this is negative f of X right there and it looks like for any x value what G of X is is one-third of that so instead of getting to four we're getting to a little bit over 1 instead of getting to 3 right over here we're two one instead of getting to one right over here we are only getting to one third so it looks like it is one third of this line that I just hand drew which is negative f of X would be one-third of negative f of X which would be negative one-third f of X once again not a choice here but let's actually look at some values so if we said let's see some values where it looks like we're hitting enter integer values so right at so for example right at this point right over here it looks like f of f of negative seven is equal to negative one it looks like G of negative seven is right so it looks like G of negative seven is equal to positive one-third positive one-third if I'm just if I'm just eyeballing it so that seems consistent with this because if F of if F of negative 7 is negative one you take the negative one-third times that and you get positive one third we could do that a couple of other places if we look right over if we look right over here it looks like F of negative one F of negative one is equal to negative three and it looks like G of 1 is negative 1/3 times that negative one-third times that is that point right over there negative 1/3 times negative 3 is positive one so G of G is color in that red color so we get for that point right over there we get G of negative one is equal to positive one so once again this is negative 1/3 times this right over here so I put I feel pretty confident of my answer G of X is equal to negative 1/3 times f of X once again negative f of X would just flipped over and then multiplying it by the 1/3 diminishes that which we see right over there so I feel pretty confident with my none of the above