![]() ![]() The above matrix A reflects a point (defined by column vector x) over the x-axis. In the Cartesian plane, a 2 x 2 matrix can describe a transformation on the plane. Matrix Operation for Reflection Over The X-Axis The important part of the formula is the expression on the right hand side. Note: I’m using f(x) and g(x) here to name the functions, but you can name them anything you like (or use whatever names your instructor is using). Step 3: (Optional) Check your work by graphing both functions (your original function from the question and the one from Step 2) to make sure they are perfect reflections (I used ): Step 2: Remove the parentheses, carrying through the negative sign: Step 1: Place a negative sign in front of the right-hand side of the function:į(x) = x 2 – 3 becomes g(x) = – (x 2 – 3) Reflection in the line x 0 i.e., in 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). When a function f(x) is reflected over the x-axis, it becomes a new function g(x) = – f (x).Įxample Question #2: What is f(x) = x 2 – 3 reflected over the x-axis? The objects appear as if they are mirror reflections, with right and left reversed. To reflect a function over the x-axis, multiply it by negative 1 (usually just written as “-“). ![]() You can easily do this on : Just enter coordinates into the left hand column and check the “Label” box: ![]() Step 2: (Optional) Plot both sets of coordinates (your original points and the ones from Step 2) to make sure you negated correctly. Step 1: Place a negative sign in front of each y-coordinate: If you have a set of coordinates, place a negative sign in front of the value of each y-value, but leave the y-value the same.Įxample question #1: Reflect the following set of coordinates over the x-axis: Reflection Over The X-Axis: Sets of Coordinates Then write the new vertices of the two new images. Every point above the x-axis is reflected to its corresponding position below the x-axis Every point below the x-axis is reflected to its corresponding position above the x-axis.ġ. Graph DOG and its reflection over the y axis and over the x axis. Reflection over the x-axis is a type of linear transformation that flips a shape or graph over the x-axis. Feel like "cheating" at Calculus? Check out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book. ![]()
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