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3 years ago

Give an example of an odd function and explain algebraically why it is odd. (3 points)

Mathematics

2 answers:

MrRissso [65]3 years ago

4 0

Answer: $f(x)=5x^{3}-x$

Step-by-step explanation:

1. By definition, algebraically, a function is odd when:

$-f(x)=f(-x)$

2. Therefore, if you have the following function:

$f(x)=5x^{3}-x$

You can know if it is odd by substituting $x=-x$ :

$f(-x)=5(-x)^{3}-(-x)$

$f(-x)=-5x^{3}+x$

3. $-f(x)$ is:

$-f(x)=-5x^{3}+x$

4. Then, as $-f(x)=f(-x)$ it is odd

klio [65]3 years ago

3 0

Answer:

See below

Step-by-step explanation:

In an odd function f(-x) will equal -f(x).

An example is f(x) = x^3:-

f(-x) = (-x)^3 and -f(x) = -x^3:-

(-x)^3 = -x * -x * -x = -x^3.

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Julie and mark are selling wrapping paper for a school fundraiser. Julie sold 13 rolls of plain wrapping paper and 8 rolls of ho

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Answer:

Cost of one roll of plain wrapping paper is $12 and Cost of one roll of holiday paper is $17.

Step-by-step explanation:

Solution,

Let the cost of 1 plain wrapping paper be x.

And the cost of 1 holiday paper be y.

Julie sold 13 rolls of plain wrapping paper and 8 rolls of holiday paper and earns $292.

Total Money earned by Julie is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

$13x+8y=292\ \ \ \ \ equation\ 1$

Now, Mark sold 7 rolls of plain wrapping paper and 2 rolls of holiday paper and earns $118.

Total Money earned by Mark is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

$7x+2y=118\ \ \ \ \ equation\ 2$

Now Multiplying equation 2 by 4 we get;

$4(7x+2y)=118\times4\\\\4\times7x+4\times2y=118\times4\\\\28x+8y= 472 \ \ \ \ equation\ 3$

Now Subtracting equation 1 from equation 3.

$(28x+8y)-(13x+8y)= 472-292\\\\28x+8y-13x-8y= 180\\\\15x=180\\\\x=\frac{180}{2} = \$12$

Now substituting the value of x in equation 1 we get;

$13x+8y=292\\\\13\times12+8y=292\\\\156+8y=292\\\\8y=292-156\\\\8y=136\\\\y=\frac{136}{8}= \$17$

Hence Cost of one roll of plain wrapping paper is $12 and Cost of one roll of holiday paper is $17.

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