![]() ![]() What happens to the graph of this equation if every “x” in the equation is replaced by a value that is 4 less? We can describe this algebraically by evaluating instead of, and let’s call this new function : This process works for any function, and is usually thought through in the reverse order: when looking at a more complex function, do you see a constant added or subtracted? If so, you can think of it as a vertical translation of the rest of the function:Ĭonsider the same function described at the beginning of the V ertical Translation section, which describes a line that passes through the origin with a slope of two: Since produces the y-coordinate corresponding to x for every point on the original graph, adding 3 to each value moves every point on the graph up by 3.Īdding “+3” to the definition of causes the entire function to be “translated vertically” by a positive three. If we then substitute the definition of from above for, we get: What happens to the graph of this line if every value of has three added to it? The function is defined as the result of with three added to each result. Vertical TranslationĬonsider the equation that describes the line that passes through the origin and has a slope of two: Before you dive into the explanations below, you may wish to play around a bit with the green sliders for “h” and “k” in this Geogebra Applet to get a feel for what horizontal and vertical translations look like as they take place (the “a” slider dilates the function, as discussed in my Function Dilations post). Which is the blue curve on the graph above, can be described as a translation of the graph of the green curve above:ĭescribing as a translation of a simpler-looking (and more familiar) function like makes it easier to understand and predict its behavior, and can make it easier to describe the behavior of complex-looking functions. In the text that follows, we will explore how we know that the graph of a function like ![]() Move the graph straight up or down in the direction of the vertical axis, and you are translating the graph vertically. ![]() If you move the graph left or right in the direction of the horizontal axis, without rotating it, you are “translating” the graph horizontally. Imagine a graph drawn on tracing paper or a transparency, then placed over a separate set of axes. A function can be translated either vertically, horizontally, or both. Other possible “transformations” of a function include dilation, reflection, and rotation. For the approach I now prefer to this topic, using transformation equations, please follow this link: Function Transformations: TranslationĪ function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |