SOLUTION: Which of the following functions are even? I 3y=(x^4)+x II y= abs(x-2) *abs= absolute value III (e^x^2)-1 This is a multiple choice question, the answer choices be

Algebra ->  Rational-functions -> SOLUTION: Which of the following functions are even? I 3y=(x^4)+x II y= abs(x-2) *abs= absolute value III (e^x^2)-1 This is a multiple choice question, the answer choices be      Log On


   

Question 889661: Which of the following functions are even?
I 3y=(x^4)+x
II y= abs(x-2) *abs= absolute value
III (e^x^2)-1
This is a multiple choice question, the answer choices being,
a. I only
b. II only
c. III only
d. II and III
e. I,II, and III
using my graphing calculator I got I and III which is not an answer but algebraically I got III only, is this correct? Thank you so much for your time and help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For an even function, f%28x%29=f%28-x%29
I. 3y=x%5E4%2Bx
f%28x%29=%281%2F3%29%28x%5E4%2Bx%29
f%28-x%29=%281%2F3%29%28x%5E4-x%29
So I is not an even function.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%281%2F3%29%28x%5E4%2Bx%29%29
.
.
.
II. I assume you mean f%28x%29=abs%28x-2%29%2Aabs%28x%29
f%28-x%29=abs%28-x-2%29%2Aabs%28-x%29
Although abs%28x%29=abs%28-x%29, it's not the case that,
abs%28-x-2%29=abs%28x-2%29
So II is not an even function.
It is symmetric but not about the y-axis but about x=2.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cabs%28x-2%29%2Aabs%28x%29%281%2F3%29%29
.
.
.
III. f%28x%29=e%5E%28x%5E2%29-1
f%28-x%29=e%5E%28x%5E2%29-1
So III is an even function.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Ce%5E%28x%5E2%29-1%29
.
.
The solution is c.