Just as multiplying a function by a constant stretches or shrinks the graph vertically, multiplying the x-value by a constant before applying the function will stretch or shrink the graph horizontally. Left 3 units, which may be opposite to the direction you expected.ģ.2.2 Use your calculator to experiment and find the function that will shift
The fixed output of y = 0 was produced by x = 0 in Y 1 and was produced by x = -3 in Y 2. With the basic absolute value function and compare the x-values that produce a specific y-value.ĭisplay the table of values for Y 1 = abs(X) and Y 2 = abs(X + 3). When describing a horizontal shift, it is helpful to see which x-values produce the same y-value. It should seem reasonable to conclude that when you add a constant to the x-values, the transformation will be a horizontal shift. Recall that when a constant was added to the y-values, the transformation was a vertical shift. We will now examine the effect of adding to (or subtracting from) the x-values before applying the function.
In each case, we described how the transformed graph's y-values were related to the corresponding y-values of the original function. We have examined vertical transformations that were created by stretching or shrinking vertically, by reflecting across the x-axis, or by shifting upward or downward. The table and diagram below illustrate the vertical shift of 3 units upward.Īnd describe the transformations. The transformed graph is a vertical shift of Notice that the values in Y 2 are three more than the values in Y 1. Explore the effect of adding three to the absolute value function.Įnter Y 1 = abs(x) and Y 2 = abs(x) + 3 in the Y= editor. This lesson will introduce translations, a third type of transformation, and discuss the effects of combining several types of transformations.Ī translation sends all points of a graph the same distance in the same direction.Ī vertical translation, or vertical shift, moves every point on a graph up or down the same distance. Lesson 3.1 discussed two types of transformations: stretches and reflections. Lesson 3.2: Translations and Combined Transformations Module 3 - Functions and Transformations - Lesson 2 Module 3 - Functions and Transformations
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