Graph of P(x) Under |y| Transformations: a & b

In summary, a graph of P(x) under |y| transformations is a V-shaped graph that has been transformed using absolute value operations on the y-axis. The value of "a" in the equation determines the steepness of the graph, while the "b" value determines its position on the y-axis. The graph can have multiple V-shaped curves, and to sketch it, you need to determine the values of "a" and "b" and plot the points accordingly.
  • #1
twicesana
1
0
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!
 
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  • #2
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!
What is |3|?

What is |-3|?

So given \(\displaystyle y \geq 0\) what happens to |y|? etc.

-Dan
 
  • #3
transformation sketch ...
 

Related to Graph of P(x) Under |y| Transformations: a & b

1. What is a graph of P(x) under |y| transformations?

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.

2. What is the purpose of using |y| transformations on a 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.

3. How do you perform a |y| transformation on a graph of P(x)?

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.

4. What are the effects of a and b on a graph of P(x) under |y| transformations?

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.

5. Can a graph of P(x) under |y| transformations have multiple transformations applied?

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.

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