How do you show a reflection over the x-axis in an equation?
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How do you show a reflection over the x-axis in an equation?
Reflection across the x-axis: y = − f ( x ) y = -f(x) y=−f(x) The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. The only difference is that, rather than the y-axis, the points are reflected from above the x-axis to below the x-axis, and vice versa.
Can every translation be shown as the result of two other translations?
In a translation, the figure is moved in a single direction without turning it or flipping it over. A translation can, of course, be combined with the two other rigid motions (as transformations which preserve a figure’s size and shape are called), and it can in particular be combined with another translation.
How do you know when to reflect over the x-axis?
What is the rule for a reflection across the X axis? The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
What is the rule for the reflection RY X x Y → Y X?
Notation Rule A notation rule has the following form ry−axisA → B = ry−axis(x,y) → (−x,y) and tells you that the image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1. Reflection A reflection is an example of a transformation that flips each point of a shape over the same line.
What is the translation rule?
A translation is a type of transformation that moves each point in a figure the same distance in the same direction. The second notation is a mapping rule of the form (x,y) → (x−7,y+5). This notation tells you that the x and y coordinates are translated to x−7 and y+5. The mapping rule notation is the most common.
Can all translations be expressed in terms of reflections?
Any translation or rotation can be expressed as the composition of two reflections. A composition of reflections over two parallel lines is equivalent to a translation. (May also be over any even number of parallel lines.) The composition of reflections over two intersecting lines is equivalent to a rotation.
Multiplying f(x) by g(x) ends up multiplying f(x) by 2, so the slope of f(x) changes by a factor of 2. In other words, the slope of h(x) is now 4. This higher slope makes h(x) steeper than f(x).