This will involve changing the coordinates.įor example, try to reflect over the -axis. In this lesson, we’ll go over reflections on a coordinate system. If k<0, it's also reflected (or 'flipped') across the x-axis. As the coefficient of x gets larger the v shape approaches. Do the same for the other points and the points are also Scaling & reflecting absolute value functions: equation Google Classroom About Transcript The graph of ykx is the graph of yx scaled by a factor of k. so you see the graph of a an absolute value function is always v shaped with a line of symmetry. When a a is greater than 1 1: Vertically stretched When a a is between 0 0 and 1 1: Vertically compressed Vertical Compression or Stretch: None Compare and list the transformations. The x values are the ones that will change, and they will be negated, meaning you will flip the sign of the x values. ![]() ![]() Figure 3-9: Vertical and horizontal reflections of a function. Count two units below the x-axis and there is point A’. Reflection about the y-axis: None Compressing and stretching depends on the value of a a. A vertical reflection reflects a graph vertically across the x -axis, while a horizontal reflection reflects a graph horizontally across the y -axis. 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. Since the reflection applied is going to be over the x-axis, that means negating the y-value. Determine the coordinate points of the image after a reflection over the x-axis. 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 see how to graph the function using transformations, long division or synthetic division on the original function must be done to obtain a more user friendly form of the equation.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. An absolute value is the numerical distance from zero and can be used in equations and graphed as dilations or reflections. The part of the graph to the left of the y axis is deleted the part to the right of the y axis remains and is reflected about the y axis. Features (of parent function): Domain: All Reals (-,) Unless domain is altered. This is a different form of the transformation. The absolute value function is one of the most recognized piecewise defined functions. ![]() And every point below the x-axis gets reflected above the x-axis. Reflection over y axis-(-x) Reflects over x and y axis. Since the line of reflection is no longer the x-axis or the y-axis, we cannot simply negate the x- or y-values. Graph functions with stretches and shrinks. When a rational function consists of a linear numerator and linear denominator, it is actually just a translation of the reciprocal function. Every point that was above the x-axis gets reflected to below the x-axis. Matthew 6:14 NIV 1-07 Transformations of Functions Summary: In this section, you will: Graph functions with translations. ![]() \(\qquad\qquad\)shift left \(2\) units, reflect over the \(x\)-axis,
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