![]() Just remember that to move in the +x direction, c needs to be negative. It is important to understand the effect such constants have on the appearance of the graph. You may intuitively think that a positive value should result in a shift in the positive direction, but for horizontal shifts, that is not the case. Horizontal shifts Vertical shifts Horizontal dilation Vertical dilation Contributors Many functions in applications are built up from simple functions by inserting constants in various places. If c is positive, the function will shift to the left by c units. If c is negative, the function will shift right by c units. Horizontal shifts correspond to the letter c in the general expression. In the general form of function transformations, they are represented by the letters c and d. It has been dilated (or stretched) horizontally by a factor of 3. The red curve in the image above is a transformation of the green one. Dilations change the shape of a graph, often causing movement in the process. A vertical compression pushes things toward the x axis, so a vertical compression will look the same as a horizontal stretch, and a vertical stretch will look like a horizontal compression. Translations move a graph, but do not change its shape. They are one of the most basic function transformations. No, stretching is like pulling either up (vertical) or out (horizontal). These shifts occur when the entire function moves vertically or horizontally. Replacing a, b, c, or d will result in a transformation of that function. Horizontal shift can be counter-intuitive (seems to go the wrong direction to some people), so before an exam (next time) it is best to plug in a few values and compare the shifted value with the parent function. Generally, all transformations can be modeled by the expression: Horizontal shift for any function is the amount in the x direction that a function shifts when c 0. Home / algebra / function / function transformations Function transformationsįunction transformations describe how a function can shift, reflect, stretch, and compress. ![]()
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