Reflection over the y axis: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). Reflection over the x-axis: When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). The reflection of the point (x, y) across the line y= -x is the point (-y, -x). The reflection of the point (x, y) across the line y=x is the point (y, x). The y-coordinate will be the midpoint, which is the average of the y-coordinates of our point and its reflection. To do this for y 3, your x-coordinate will stay the same for both points. If you forget the rules for reflections when graphing, simply fold your paper along the x -axis (the line of reflection) to see where the new figure will be located. If you reflect over the line y=-x, the coordinate and y-coordinate change places and are negated (the signs are changed). The closest point on the line should then be the midpoint of the point and its reflection. Reflect over the x-axis: When you reflect a point across the x -axis, the x- coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Reflect over the y=x: When you reflect a point across the line y=x, the coordinate and y-coordinate change places. 29 Example 8.2 Find the equation of the line produced by y 2x - 3 when it is reflected in the line y x, Solution As y 2x - 3 and its reflection y. The reflection of the point (x, y) across the y-axis is the point (-x, y). Reflect over the y axis: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). The reflection of the point (x, y) across the x-axis is the point (x, -y). 3 Answers Sorted by: 3 Adding to Adriano's answer, if you want to reflect y f(x) y f ( x) across y mx + b y m x + b you have to reflect the function by the x-axis and then rotate it by + 2tan1(m) + 2 tan 1 ( m) radians. Reflect over the x-axis: When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). Transformations are used to change the graph of a parent function into the graph of a more complex function.So, the reflection of point B (3, -4) along the y-axis is (-3, 4). If a reflection is about the y-axis, then, the points on the right side of the y-axis gets to the right side of the y-axis, and vice versa. Stretching a graph means to make the graph narrower or wider. They are caused by differing signs between parent and child functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider. Reflections are transformations that result in a "mirror image" of a parent function. 14 c(x,y,z) here p1,2., denoting sequential number of the strada, y-axis. Reflecting a graph means to transform the graph in order to produce a "mirror image" of the original graph by flipping it across a line. (1.50c) The above equations are not typical acoustic equations and must be. All other functions of this type are usually compared to the parent function. Solution The equation becomes y (2(x 2))4 x4 to obtain the graph y 5 5. Sketch the graph of each of the following transformations of y = xĪ stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.įunction families are groups of functions with similarities that make them easier to graph when you are familiar with the parent function, the most basic example of the form.Ī parent function is the simplest form of a particular type of function. a reflection in the y-axis (b < 0), a horizontal stretch from the y-axis by a factor of (lbl 2), a horizontal translation to the right 2 units (h 2), and Applying Transformations Example 2 Describe the transformations applied to y state the domain and range. Graph each of the following transformations of y=f(x). Let y=f(x) be the function defined by the line segment connecting the points (-1, 4) and (2, 5).
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