# Math Help - Symmetry

1. ## Symmetry

Determine whether the graph of the function is symmtetric about the y-axis, the origin, or neither.

y= x^2 - 2x - 1

Is it simply just plugging in -x for the values of x and all that jazz? The other one was y=x^(1/5). I found out that f(-x) = -f(x) so it was an odd function and symmetric with the origin. What's going on in the x^2 example?>

2. Originally Posted by fezz349
Determine whether the graph of the function is symmtetric about the y-axis, the origin, or neither.

y= x^2 - 2x - 1

Is it simply just plugging in -x for the values of x and all that jazz? The other one was y=x^(1/5). I found out that f(-x) = -f(x) so it was an odd function and symmetric with the origin. What's going on in the x^2 example?>
yes ... given that you understand the jazz.

$f(x) = x^2 - 2x - 1$

$f(-x) = (-x)^2 - 2(-x) - 1 = x^2 + 2x - 1$

does $f(-x) = f(x)$ or $-f(x)$ ?

if no, then no symmetry.

3. Ok thanks a lot man, I can see that it doesn't equal to f(x), but i'm just not understanding it with the -fx . in the equation x^2 - 2x - 1 i don't understand what's going on with the "x" in the 2x? the x in x^2 becomes -x^2 with no parentheses, what about the second one?

4. Originally Posted by fezz349
Ok thanks a lot man, I can see that it doesn't equal to f(x), but i'm just not understanding it with the -fx . in the equation x^2 - 2x - 1 i don't understand what's going on with the "x" in the 2x? the x in x^2 becomes -x^2 with no parentheses, what about the second one?
$f(x) = x^2 - 2x - 1$

$-f(x) = -(x^2 - 2x - 1)$

... change the signs

$-f(x) = -x^2 + 2x + 1$