Question

Odd even or neitheer

how many mistakes i have explain it to me​

Answer 1

1. neither
2. odd
3. odd
4. even
5. even
6. neither
7. even
8. even

Explanation:

You want to classify a number of functions as even, odd, or neither.

Even Function

An even function has a graph that is symmetrical about the y-axis. It has the characteristic that ...

f(x) = f(-x)

A polynomial function will be an even function if it consists entirely of even-degree terms. (A constant is degree zero, hence even degree.) A rational function will be an even function if it can be reduced to the ratio of even functions.

Odd Function

An odd function has a graph that is symmetrical about the origin. It has the characteristic that ...

f(x) = -f(-x)

A polynomial function will be an odd function if it consists entirely of odd-degree terms. A rational function will be an odd function if it reduces to the ratio of an even and an odd function.

Neither

A function is neither even nor odd if it does not have one of the symmetries mentioned above. A polynomial consisting of a mix of even- and odd-degree terms will be neither even nor odd.

1. (x³+4x²)/(7x²+1)

This is the ratio of a "neither" function to an even function. It is neither even nor odd.

2. (2x⁴+8x³)/(x³+4x²)

The ratio can be reduced to ...

`(2x^4+8x^3)/(x^3+4x^2)=(2x^3(x+4))/(x^2(x+4))=2x`

This consists only of an odd-degree term. It is an odd function.

3. x³/(7x²+1)

This is the ratio of an odd function to an even function. It is an odd function.

4. (4x²+7)/(7x⁸+3x²)

This is the ratio of two even functions. It is an even function.

5. (2x³+8x²)/(x³+4x²)

As in problem 2, the function can be reduced:

`(2x^3+8x^2)/(x^3+4x^2)=(2(x^3+4x^2))/(x^3+4x^2)=2`

It is an even (degree 0) function.

6. (x²-4)/(x-2)

This is the ratio of an even function to a "neither" function. It is neither even nor odd.

The function reduces to x+2, which is neither even nor odd.

7. 1/(x²+9x⁶)

This is the ratio of two even functions. It is an even function.

8. (4x³+2x)/(7x⁵+3x³)

This is the ratio of two odd functions. It can be reduced to the ratio of two even functions, so it is an even function.

`(4x^3+2x)/(7x^5+3x^3)=(2x(2x^2+1))/(x^3(7x^2+3))=(4x^2+2)/(7x^4+3x^2)`