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SHIFTS IN A GRAPH There are three possible shifts in a graph. A shift is a transformation that moves a graph up or down (vertical) and left or right (horizontal). There is vertical shrinking or vertical stretching, horizontal shifts, and vertical shifts that are possible for a graph.Vertical shrinking or vertical stretching is a nonrigid transformation. This means that the graph causes a distortion, or in other words, a change in the shape of the original graph. Shifting and reflections are called rigid transformations because the shape of the graph does not change. Vertical stretches and shrinks are called nonrigid because the shape of the graph is distorted. Stretching and shrinking change the distance a point is from the x-axis by a factor of c. For example, if g(x) = 2f(x), and f(5) = 3, then (5,3) is on the graph of f. Since g(5) = 2f(5) = 2*3 = 6, (5,6) is on the graph of g. The point (5,3) is being stretched away from the x-axis by a factor of 2 to reach the point (5,6).Let c be a positive real number. Then the following are vertical shifts of the graph of y = f(x) a) g(x) = cf(x) where c>1. Stretch the graph of f by multiplying its y coordinates by c If the graph of is transformed as: 1. , then the graph has a vertical stretch.2. , then the graph has a vertical shrink.3. , then the graph has a horizontal shrink.4. , then the graph has a horizontal stretch.Graphs also have a possible horizontal shift. This is a rigid transformation because the basic shape of the graph is unchanged. In the example y = f(x), the modified function is y = f(x-a), which results in the function shifting a units....

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