Determining if a function is even, odd or neither...

[Math_Junkie]

I'm doing some problems for homework, and I got stuck on the following 2 functions.

1. f(x) = 2x^2 - x
2. g(x) = |2x + 3|

Are these functions even, odd or neither? Any extra help would be appreciated.

 

[mmm4444bot]

Do you know the definitions?

Hello Math Junkie:

Will you please let us know why you're stuck? It's hard for me to guess what you would like anybody to do for you regarding these exercises.

You should start by looking up the definitions for even and odd functions.

There are different ways to answer these exercises. One can complete them algebraically or graphically.

The algebraic method requires you to see what happens if you change the sign on the functions' input.

The graphical approach can be done in your head and explained in words.

Do you know how to complete the square on the output of f(x)?

Have you learned about transformations (i.e., shifting graphs)?

Are you familiar with parabolas?

Are you familiar with graph of absolute value?

Do you understand symmetry on the xy-coordinate system?

Have you tried determining how the function output changes if you change the sign on the input?

In other words, did you try the following?

f(-x) = ?

g(-x) = ?

Are you having trouble understanding your textbook?

Do you need help finding lessons on the Internet?

I'm not motivated to type up a dozen lessons, so why don't you post your work?

Please let us know what you already know. If you could ask a specific question about how to answer these exercises, that would be great.

You should start by looking up the definitions for even and odd functions.

Cheers,

~ Mark

 

[Math_Junkie]

I just wanted to make sure I was doing the questions right.

I know that these are the equations for determining whether a function is odd or even:
Even: f(x) = f(-x)
Odd: f(-x) = -f(x)
The problem is, I'm unsure if I'm using the equations properly.

But anyway for quesion 1, f(x) = 2x^2 - x, I did..

Even:
f(x) = f(-x)
2x^2 - x = 2(-x)^2 + x
2x^2 - x = 2x^2 + x
Not even.

Odd:
f(-x) = -f(x)
2x^2 - x = -(2x^2 - x)
2(-x)^2 - x = -2x^2 + x
-2x^2 - x = -2x^2 + x
Not odd.

Therefore the function must be neither?

For question 2, I'm not sure how to handle the absolute value bars, so a sample solution would help me greatly.

 

[mmm4444bot]

Re: Do you know the definitions?

I just wanted to make sure I was doing the questions right.

Hmmm, I'm not sure why you would expect anybody here to realize from your original post that you just want us to check your work on exercise 1, but thanks for cluing us in.

... for quesion 1, f(x) = 2x^2 - x, I did..

Even:
f(x) = f(-x)
2x^2 - x = 2(-x)^2 + x
2x^2 - x = 2x^2 + x
Not even. ? Correct

Odd:
f(-x) = -f(x)
2x^2 - x = -(2x^2 - x) ? The expression in red is not f(-x)
2(-x)^2 - x = -2x^2 + x ? The expression in red is not f(-x)
-2x^2 - x = -2x^2 + x
Not odd. ? Correct

Therefore the function must be neither? Why are you asking us this? Are you still not sure?

Regarding exercise 2, do you know enough about absolute value to tell me whether or not the following statement is true?

|7 - 4x| = |4x - 7|

If you understand this, then go ahead and try the same method you used on exercise 1.

Please show us your work if you need more assistance!

Cheers,

~ Mark