![]() In order to translate any of the common graphed functions, you need to recall and be fluent with the seven common functions themselves, presented here alphabetically because they are all equally important:Ībsolute Value Function: y = ∣ x ∣ y=\left|x\right| y = ∣ x ∣Ĭubic Function: y = x 3 y= y = x īy concentrating on the original seven functions and the way they appear when graphed, you will soon develop an awareness of how each of the three translations affects the original graphed function. Knowing how to shift, scale or reflect these graphs makes you a stronger mathematics student and produces many variations on the original graphs of common functions. Shifting, scaling and reflecting are three methods of producing translations for basic graphing functions you have already learned. Reflection - A mirror image of the graph of a function is generated across either the x-axis or y-axis ![]() Scale - The size and shape of the graph of a function is changed Shift - The graph of a function retains its size and shape but moves (slides) to a new location on the coordinate grid Translations are performed in three ways: Then, using translations, you can move the point. Using the abscissa and ordinate, you can fix a point on the coordinate graph. This is the distance above or below the x-axis. Its partner is the ordinate, or y-coordinate. We got it right.The abscissa is the x-coordinate, or the distance left or right from the y-axis that allows you to locate a point using a coordinate pair. Of that target triangle that they asked me to map to, to translate to. I was able to, through the translation, the image is now in kind And I was able to get onto this triangle. ![]() To the left by seven, and has been shifted down by four. To successfully translate it by translating x by negative seven, every point here, every point on this has been shifted What happens? And it looks like I was able And now, in the y axis, I need to move it down by, let's see, one, two, three, four. Negative seven, and then, let's see, on the y side, and we saw that, by just typing in negative seven, here we moved it to the left by seven. So my x would have to decrease by seven, so let me type that in. How much do we translate the x coordinates, and how much do we translate the y coordinates? Let's see, if I want to map, if I want to get point W to correspond to this point right over here, which it seems like it should, I would have to go from x equals two, to x equals negative five. So it says translate by, and this is gonna say so To use the translation tool to determine the translation that will map triangle WIN, so this right over here, onto the other triangle. Tell me if you're still confused and need me to simplify this again. Sorry if this was long and a bit complicated. ![]() And because he moved down it's negative so the y coordinate is -4(If he moved up then it would be positive). Because he moved left, it's a negative so the x coordinate is -7(If it was to the right then it would be positive). He does this by solving for their coordinates (x,y) (x(horizontal) always comes before the y(vertical)). Here, Sal translates the blue triangle to fit in the gray triangle. It's the same thing with figures on a coordinate plane. You're still yourself, you haven't changed anything about yourself but you just changed positions. Say you're in your house but then you go outside. The figure still has the same size, you're just moving it in a different place. A translation is just moving a figure to a different place on a coordinate grid. ![]()
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