determine if the following function is odd, even or neither
g(x)=|-x|
and
f(x)=|2x+2|
(and those | are absolute value not 1)
I really don't know, please help
thank you
The g(x)=l-xl is just functions(look it up). So, G(x) is equal to x, to get rid of the - sign. Then, we go to the f(x). f(x) is 2x+2, and they are already in absolute form. You really can't determine if the functions are even or odd, because x is an unknown number in g(x). In f(x), any whole number that is a whole number multiplied by 2 is even, but because we don't know x is, we can't really specify it. So, they are all neither. That's it!
+130511 g(x) = l -x l
Note that this can actually be written as l -1 * x l = l -1 l * l x l = 1 * l x l = l x l (1)
So.....to see if this is an even function, we would replace x with -x and have
l - (-x) l = l x l which is exactly the same thing as (1)....so...this function is even
Also...look at the graph : https://www.desmos.com/calculator/yoopdzrkic
The symmetric nature of the graph with respect to the y axis is a trademark of an even function
f(x) = l 2x + 2]
To test if this is an even function, replace x with -x and we have l 2(-x) + 2 l = l -2x + 2 l which is definitely not what we started with....so.....this function is not even
And it is not odd either, because f(-x) would have to equal -f(x) = - l 2x + 2 l for this to be an odd function
Also...look at the graph : https://www.desmos.com/calculator/wlnt4se3nw
Odd functions are symmetric about the origin.....however, this graph is not symmetric about the origin!!!
