Try to find the closest distance between the two. Of an optical illusion- it looks like they So it looks like if we pickĪny point over here- even though there's a little bit ![]() ![]() Write this down- g of 2 is equal to f of 2 plus 1. And we see that, at leastĪt that point, g of x is exactly 1 higher than that. Hope I didn't over explain, just proud of what I made tbh so 5*f(x) would make a point (2,3) into (2,15) and (5,7) would become (5,35)ī will shrink the graph by a factor of 1/b horizontally, so for f(5x) a point (5,7) would become (1,3) and (10,11) would become (2,11)Ĭ translates left if positive and right if negative so f(x-3) would make (4,6) into (7,6) and (6,9) into (9,9)ĭ translates up if positive and down if negative, so f(x)-8 would make the points (5,5) and (7,7) into (5,-3) and (7,-1)Īlso should note -a flips the graph around the x axis and -b flips the graph around the y axis. So for example if f(x) is x^2 then the parts would be a(b(x+c))^2+dĪ will stretch the graph by a factor of a vertically. Then if m is negative you can look at it as being flipped over the x axis OR the y axis.įor all other functions, so powers, roots, logs, trig functions and everything else, here is what is hopefully an easy guide. ![]() Yep, for linear functions of the form mx+b m will stretch or shrink the function (Or rotate depending on how you look at it) and b translates.
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