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You guys are great! 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. We used this method to help transform a piecewise function here. Also, the last type of function is a rational function that will be discussed in the Rational Functions section. Easy way to remember: You might be asked to write a transformed equation, give a graph.
A lot of times, you can just tell by looking at it, but sometimes you have to use a point or two.
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