![]() ![]() An odd function either passes through the origin (0, 0) or is reflected through the. This kind of symmetry is called origin symmetry. This time, if we reflect our function in both the x -axis and y -axis, and if it looks exactly like the original, then we have an odd function. ![]() How do you reflect over Y -2 To reflect over the line Y -2, you apply the reflection rule: (x, y) (x, -2 (y (-2))). ![]() It means that each point’s x-coordinate remains the same, but the y-coordinate changes sign. If the negative sign belongs to the x, then the graph will flip about the y-axis. An odd function has the property f(x) f(x). A horizontal reflection over the y-axis is a transformation that flips a shape or point horizontally across the y-axis. If the negative sign belongs to the y, then the graph will flip about the x-axis. Remember Reflections: They appear like opposites Example: y = | –x| will flip the function about the y-axis If the negative sign belongs to the x-value the graph will reflect about the y-axis. Other important transformations include vertical shifts, horizontal shifts and horizontal compression. A math reflection flips a graph over the y-axis, and is of the form y f (-x). In this example, flipping the original function across the y-axis is identical to the original graph (so it looks like nothing happened). If we get the same function from a math reflection, it is a symmetrical function, specifically even. At first the two functions might look like two parabolas.If you graph by hand, or if you set your calculator to sequential mode (and not simultaneous), you can see that the graph of y -x 3 is in fact a reflection of y x 3 over the x-axis. Example: y = –|x| will flip the function about the x-axis If the negative sign belongs to the y-value the graph will reflect about the x-axis.ĭo you see how the negative sign is on the inside of the function… affecting the x-value of the function? When you apply a negative to each x-coordinate of each point (-x,y), the graph flips across the y-axis. Sketch a graph of y x 3 and y -x 3 on the same axes. Question: What does a negative do to a graph? Answer: Multiplying a function by a negative sign creates a reflection: y = –f(x) or y = f( –x)įLIPS FUNCTIONS ABOUT THE X-AXIS y = –f(x)ĭo you see how the negative sign is on the outside of the function… affecting the y-value of the function? When you apply a negative to each y-coordinate of each point (x,-y), the graph flips across the x-axis. ![]()
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