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

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The graph of P(x) = 3x + 4 behaves differently under the transformation y = |P(x)| based on the value of y. For y ≥ 0, the graph remains unchanged since the output is already non-negative. However, for y < 0, the transformation reflects the negative portions of the graph above the x-axis, resulting in a V-shaped graph that only shows non-negative values. This transformation effectively eliminates any negative y-values by mirroring them. Understanding these behaviors is crucial for analyzing the effects of absolute value transformations on linear functions.
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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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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 [math]y \geq 0[/math] what happens to |y|? etc.

-Dan
 
transformation sketch ...
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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