More References and Links to Graphing Graphing Functions. Following figures shows the reflection of the object axis. Graph in blue is that of f(x) = |x| and the graph in red is that of g(x) = 2 |x| In this transformation value of x will remain same whereas the value of y will become negative. Take any function f(x), the graph of k f(x) (with k > 0) will be the graph of f(x) expanded vertically if k is greater than 1 and compressed vertically if k is less than 1. Take any function f(x) and it to - f(x), the graph of - f(x) will be the graph of f(x) reflected on the x axis. Take any function f(x) and change x to - x, the graph of f(- x) will be the graph of f(x) reflected on the y axis. If c is negative, the graph is translated down as shown in the graph below. Vertical and horizontal reflections of a function. A vertical reflectionreflects a graph vertically across the x-axis, while a horizontal reflectionreflects a graph horizontally across the y-axis. If c is positive, the graph is translated up as shown in the graph below. Another transformation that can be applied to a function is a reflection over the x or y-axis. If we add a constant c to f(x), the graph of f(x) + c will be the graph of f(x) translated (or shifted) vertically. The example of the graph of f(x) = √(x) and g(x) = √(x + 2) are shown below and it is easily seen that the graph of √(x + 2) is that of √(x) shifted 2 units to the left. If c is positive, then the graph is shifted to the left. The example of the graph of f(x) = x 2 and g(x) = (x - 2) 2 are shown below and it is easily seen that the graph of (x - 2) 2 is that of x 2 shifted 2 units to the right. If c is negative, then the graph is shifted to the right. Take any function f(x) and change x to x + c, the graph of f(x + c) will be the graph of f(x) shifted horizontally c units. Triangle, triangle ABC, onto triangle A prime B prime C prime.Graphing by Translation, Scaling and ReflectionĪ step by step tutorial on the properties of transformations such as vertical and horizontal translation (or shift) The line of reflection that reflects the blue Units above this line, and B prime is six units below the line. Have here is, let's see, this looks like it's six A prime is one, two, three,įour, five units below it. A is one, two, three,įour, five units above it. C is exactly three units above it, and C prime is exactly So C, or C prime isĭefinitely the reflection of C across this line. If this horizontal line works as a line of reflection. This three above C prime and three below C, let's see So let's see, C and C prime, how far apart are they from each other? So if we go one, two, Next, we consider the transformation of y x2 given by adding or subtracting a constant to the input x. If c is positive, the graph is shifted up, if c is negative, the graph is shifted down. It does actually look like the line of reflection. Then, the graph of y f(x) + c is that of y f(x) shifted up or down by c. But let's see if we can actually construct a horizontal line where So the way I'm gonna think about it is well, when I just eyeball it, it looks like I'm just flipped over some type of a horizontal line here. Little line drawing tool in order to draw the line of reflection. So that's this blue triangle, onto triangle A prime B prime C prime, which is this red Draw the line of reflection that reflects triangle ABC,
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