00:01
Alright, this problem is asking about symmetry for y to the fourth equals x cubed plus ten.
00:09
So before we get into that, let's talk about y -axis symmetry, origin symmetry, and x -axis symmetry.
00:23
Alright, so if you have y -axis symmetry and you had a coordinate over here in the first quadrant and it was symmetric with respect to the y -axis, the only thing i would need to do would be to negate my y, right? they call these kind of functions even, alright? and when you plug in negative x into your function, you should get your original function, alright? now if i have something in the first quadrant and i say it's symmetric with respect to the origin, it goes across and over, so it comes down into the third quadrant.
01:07
So when i negate my x, i will also negate my y.
01:15
These types of functions are called odd.
01:19
So i would either get my original when i plug in negative x, or i get opposite my original for my odd.
01:34
So even functions and odd functions.
01:37
Now if i have x -axis symmetry and something is again in the first quadrant, it would be symmetric with respect to that x -axis, my x -value is going to stay the same and my y -value negates.
01:51
And when you flip this over the x -axis, reflect it over that, this is not a function.
01:57
So it doesn't have a name.
01:59
It's not odd, it's not either, even, it's neither, alright? so this one isn't a function, so kind of interesting, right? and then neither would be none of these, right? so let's go back to our original function again.
02:20
What i would do is i would solve for y.
02:24
So i would have to take the fourth root of all of this.
02:28
And when i do that, i'm going to get y equals the fourth root of x -cubed plus 10...