![]() ![]() Recall that the absolute value of a number is its distance from 0 on the number line. This will involve changing the coordinates.įor example, try to reflect over the -axis.An absolute value function is a function that contains an algebraic expression within absolute value symbols. Discover how translations apply to absolute value equations, and. If we reflect in the y axis, then the x values become -x, and the line becomes ya(-x)+b, which is y-ax+b. ![]() In this lesson, we’ll go over reflections on a coordinate system. An absolute value is the numerical distance from zero and can be used in equations and graphed as dilations or reflections. Do the same for the other points and the points are also Count two units below the x-axis and there is point A’. As a result, points of the image are going to be:īy counting the units, we know that point A is located two units above the x-axis. An absolute value is the numerical distance from zero and can be used in equations and graphed as dilations or reflections. ![]() ![]() Consider the basic graph of the function: y f(x). To reflect the absolute value function over the x-axis, we simply put a negative sign before the symbol (in this case the absolute value bars). Since the reflection applied is going to be over the x-axis, that means negating the y-value. The x values are the ones that will change, and they will be negated, meaning you will flip the sign of the x values. To reflect about the x-axis, multiply f(x) by -1 to get -f(x). Note that the slope of the linear pieces are +1 on the right. Determine the coordinate points of the image after a reflection over the x-axis. y mx + b + c where the vertex is (-b/m, c) and the axis of symmetry is x -b/m. You can also negate the value depending on the line of reflection where the x-value is negated if the reflection is over the y-axis and the y-value is negated if the reflection is over the x-axis.Įither way, the answer is the same thing.įor example: Triangle ABC with coordinate points A(1,2), B(3,5), and C(7,1). To match the distance, you can count the number of units to the axis and plot a point on the corresponding point over the axis. To reflect a shape over an axis, you can either match the distance of a point to the axis on the other side of using the reflection notation. ![]()
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