What is |3|?twicesana said:QS: Explain how the graph P(x)=3x+4 behaves under the transformation y=|P(x)| when:
a) y\ge0
b) y<0
I'm not sure how to explain this in words.Thank You!
A graph of P(x) under |y| transformations is a graph of a polynomial function P(x) that has been transformed by taking the absolute value of the y-values. This transformation can result in changes to the shape, location, and orientation of the graph.
The purpose of using |y| transformations on a graph is to make the graph more visually appealing and easier to interpret. It can also help to highlight certain features of the graph, such as the minimum or maximum values.
To perform a |y| transformation on a graph of P(x), you simply take the absolute value of all the y-values in the original graph. This can be done by hand or by using a graphing calculator.
The value of a in the transformation equation y = |aP(x)| determines the vertical stretch or compression of the graph, while the value of b determines the vertical shift of the graph. A positive value of a will result in a vertical stretch, while a negative value will result in a vertical compression. A positive value of b will shift the graph upwards, while a negative value will shift it downwards.
Yes, a graph of P(x) under |y| transformations can have multiple transformations applied. Each transformation will have its own effect on the graph, resulting in a final graph that combines all of the transformations. It is important to apply the transformations in the correct order to get the desired result.