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There are several websites on the Internet that would offer you affordable packages for the service they are providing; however, they would have a hidden catch that would lead you to pay more than you actually bargained for. So the end behavior for a line with a positive slope is: T-charts are extremely useful tools when dealing with transformations of functions. Transform function 2 units to the right , and 1 unit down. When looking at the equation of the moved function , however, we have to be careful.
There are several ways to perform transformations of parent functions; I like to use t -charts , since they work consistently with ever function. The t-charts include the points ordered pairs of the original parent functions, and also the transformed or shifted points. Notice that the first two transformations are translations , the third is a dilation , and the last is a reflection.
You may find it interesting is that a vertical stretch behaves the same way as a horizontal compression, and vice versa, since when stretch something upwards, we are making it skinnier. It makes it much easier! This is what we end up with:. We do this with a t-chart. Also remember that we always have to do the multiplication or division first with our points, and then the adding and subtracting sort of like PEMDAS.
Here is the t-chart with the original function, and then the transformations on the outsides. Then the vertical stretch is 12 , and the parabola faces down because of the negative sign. The parent graph quadratic goes up 1 and over and back 1 to get two more points, but with a vertical stretch of 12 , we go over and back 1 and down 12 from the vertex.
Now we have two points to which you can draw the parabola from the vertex. Remember that the transformations inside the parentheses are done to the x doing the opposite math , and outside are done to the y.
Note that this transformation takes the original function, flips it around the y axis , performs a horizontal stretch by 2 , moves it right by 1 , and then down by 3. Draw the points in the same order as the original to make it easier! We can do this without using a t-chart , but by using substitution and algebra.
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