Causes a reflection, vertical stretch/compression
Causes a reflection: When we talk about reflections in math, we are referring to the flipping of a figure or graph over a line
Causes a reflection: When we talk about reflections in math, we are referring to the flipping of a figure or graph over a line. In the case of functions, a reflection is caused when there is a negative sign before the function. For example, if we have the function f(x) = -x, it means that every point on the graph of f(x) will be reflected across the x-axis.
Vertical Stretch/Compression: Stretching or compressing a graph involves changing the vertical size or height of the graph. A vertical stretch occurs when the function’s values are multiplied by a number greater than 1. This stretches the graph vertically. On the other hand, a vertical compression occurs when the function’s values are multiplied by a number between 0 and 1. This compresses the graph vertically.
To better understand this, let’s consider an example:
Let’s say we have the function g(x) = 2x. This function represents a vertical stretch because the values of x are multiplied by 2, causing the graph to be stretched vertically.
If we have the function h(x) = (1/2)x, then it represents a vertical compression because the values of x are multiplied by 1/2. This compresses the graph vertically.
It’s important to note that a reflection and a vertical stretch/compression can occur independently or together in a single function. For example, the function f(x) = -2x represents both a reflection and a vertical stretch because it has a negative sign for reflection and a coefficient of 2 for vertical stretching.
Remember to always consider each factor separately when investigating the effects of a function on its graph.
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