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2 years ago

9

Is F(x)= X^2(X^2+9)(X^3+2X) even or odd

1 answer:

dexar [7]2 years ago

4 0

Answer:

The function is odd.

Step-by-step explanation:

A function is even if the graph of the function is symmetric with respect to the y-axis. A function is odd if the graph of the function is symmetric with respect to the origin. To find if the function is even or odd, we're going to graph the function using DESMOS.

As you can see in the attached picture, the function is symmetric with respect to the origin. Therefore, the function is odd.

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<u>Method 1:</u>

Using regression analysis the line of best fit is: $y=\alpha +\beta x+e$

Here <em>α </em>= intercept, <em>β</em> = slope and <em>e</em> = error.

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And the formula to compute the error is:

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The regression line can be determined using the descriptive statistics mean, standard deviation and correlation.

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Here <em>r</em> = correlation coefficient = $r=\frac{Cov (x,y)}{\sqrt{\sigma^{2}_{x}\sigma^{2}_{y}} }$

$\sigma_{x}$ and $\sigma_{y}$ are standard deviation of <em>x</em> and <em>y</em> respectively.

$\sigma_{x}=\frac{1}{n}\sum (x-\bar x)^{2} \\\sigma_{y}=\frac{1}{n}\sum (y-\bar y)^{2}$

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