If the negative sign belongs to the x, then the graph will flip about the y-axis. If the negative sign belongs to the y, then the graph will flip about the x-axis. Reflection Over An Axis For example, try to reflect over the x -axis. If the pre-image is labeled as ABC, then the image is labeled using a prime symbol, such as ABC. The original object is called the pre-image, and the reflection is called the image. Remember Reflections: They appear like opposites Reflection Notation: rx-axis (x,-y) ry-axis (-x,y). A reflection can be done through y-axis by folding or flipping an object over the y axis.

Example: y = | вЂ“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. In this example, flipping the original function across the y-axis is identical to the original graph (so it looks like nothing happened). Example: y = вЂ“|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.Дo you see how the negative sign is on the inside of the functionвЂ¦ 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. When a point is reflected across the x-axis, the x-coordinates remain the same, whereas the y-coordinate changes into its opposite i.e.

Question: What does a negative do to a graph? Answer: Multiplying a function by a negative sign creates a reflection: y = вЂ“f(x) or y = f( вЂ“x)ДЇLIPS FUNCTIONS ABOUT THE X-AXIS y = вЂ“f(x)Дo you see how the negative sign is on the outside of the functionвЂ¦ 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. 13 The graph of h (x) 1 2 undergoes the following transformations: Translation of 2 units left and 3 units down, then a reflection in the x-axis, followed by a dilation of factor 3 from the x-axis, and a reflection in the y-axis.

Reflection in the y axis