Describe the similarities between a) the lines y = x and y = -x and the graphs of other odd-degree polynomial functions b) the parabolas y=x^{2} and y=-x^{2} and the graphs of other even-degree polynomial functions

Question
Polynomial graphs
asked 2021-01-07
Describe the similarities between a) the lines \(\displaystyle{y}={x}{\quad\text{and}\quad}{y}=-{x}\) and the graphs of other odd-degree polynomial functions b) the parabolas \(\displaystyle{y}={x}^{{{2}}}{\quad\text{and}\quad}{y}=-{x}^{{{2}}}\) and the graphs of other even-degree polynomial functions

Answers (1)

2021-01-08
Step 1
The graphs of the Odd Degree Polynomial Functions will depend mainly on the Leading Coefficient.
If it is Positive the graph will expand feom quadrant 3 to quadrant 1 i.e. like to the graph of \(\displaystyle{y}={x}\)
On the other hand, If it is Negative the graph will expand from quadrant 2 to quadrant 4 i.e. like to the graph of \(\displaystyle{y}=-{x}\)
Step 2
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Step 3
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Step 4 The Graphs of the Even Degree Polynomial Functions will depend mainly on the Leading Coefficient.
If it is Positive the graph will expand from quadrant 2 to quadrant 1 i.e. like to the graph of PSKy=x^{2}.
On the other hand, If it is Negative the graph will expand from quadrant 3 to quadrant 4 i.e. like to the graph of \(\displaystyle{y}=-{x}^{{{2}}}\)
Step 5
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Step 6
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Answer:
a) Graph of odd-degree polynomial functions and the lines \(\displaystyle{y}={x}{\quad\text{and}\quad}{y}=-{x}\)
b) Graph of even-degree polynomial functions and the lines \(\displaystyle{y}={x}^{{{2}}}{\quad\text{and}\quad}{y}=-{x}^{{{2}}}\)
0

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