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One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function.
The graph of a function is reflected about the \(y\)-axis if each \(x\)-coordinate is multiplied by \(−1\) before the function is applied. For example, consider \(g(x)=\sqrt{−x}\) and \(h(x)=−\sqrt{x}\).
Stretch it by 2 in the y-direction: h (x) = 2/x. Compress it by 3 in the x-direction: h (x) = 1/ (3x) Flip it upside down: h (x) = −1/x. Example: the function v (x) = x 3 − 4x. Here are some things we can do: Move 2 spaces up: w (x) = x3 − 4x + 2. Move 3 spaces down: w (x) = x3 − 4x − 3.
Function transformations refer to how the graphs of functions move/resize/reflect according to the equation of the function. Learn the types of transformations of functions such as translation, dilation, and reflection along with more examples.
These horizontal and vertical lines or axis in a graph are the x-axis and y-axis respectively. In this mini-lesson, we will learn about the x-axis and y-axis and what is x and y-axis in geometry along with solving a few examples.
Graph functions using reflections about the x-axis and the y-axis. Determine whether a function is even, odd, or neither from its graph. Graph functions using compressions and stretches.
20 Μαΐ 2024 · Graph transformations involve changing the appearance or position of graphs by shifting them horizontally or vertically, stretching or compressing them, reflecting them across axes, or rotating them around a fixed point. These modifications help visualize how functions change under different conditions or transformations.
