even/odd graph

**live_laugh_luv27** · August 9th 2009, 09:27 AM

Are the graphs of

$\sqrt{x}$

$2^x$

$log_2x$

even or odd? I don't see any symmetry with respect to y axis or origin. Thanks!

**Jhevon** · August 9th 2009, 09:40 AM

Originally Posted by live_laugh_luv27

Are the graphs of

$\sqrt{x}$

$2^x$

$log_2x$

even or odd? I don't see any symmetry with respect to y axis or origin. Thanks!

A function $f(x)$ is even if $f(-x) = f(x)$

A function $f(x)$ is odd if $f(-x) = -f(x)$

can you continue?

**live_laugh_luv27** · August 9th 2009, 10:10 AM

so,

even

odd

even

?

**live_laugh_luv27** · August 9th 2009, 10:15 AM

I'm still not exactly sure how to set that up, but have another ?...even if a function does not have symmetry in respect to the y-axis, can it still be even? similarly, even if the function does not have symmetry in respect to the origin, can it still be odd?
thanks!

**Plato** · August 9th 2009, 10:17 AM

Originally Posted by live_laugh_luv27

so,

even

odd

even

What does any of the above have to do with the basic definitions of odd & even?
$\text{Odd functions are such that }f(-x)=-f(x)$

$\text{Even functions are such that }f(-x)=f(x)$

**Jhevon** · August 9th 2009, 10:27 AM

Originally Posted by live_laugh_luv27

I'm still not exactly sure how to set that up, but have another ?...even if a function does not have symmetry in respect to the y-axis, can it still be even? similarly, even if the function does not have symmetry in respect to the origin, can it still be odd?
thanks!

no, even and odd follow the exact definitions i gave you. you don't even have to look at the graphs.

example, state whether (a) $f(x) = x^2$ , (b) $f(x) = \sin x$ and (c) $f(x) = \frac {x^2}{x^3 + 1}$

(a) $f(x) = x^2$ is even, since

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

(b) $f(x) = \sin x$ is odd, since

$f(-x) = \sin (-x) = - \sin x = - f(x)$

(c) $f(x) = \frac {x^2}{x^3 + 1}$ is neither even nor odd, since

$f(-x) = \frac {(-x)^2}{(-x)^3 + 1} = \frac {x^2}{1 - x^3} \ne f(x) \text{ or } -f(x)$

notice that i didn't even draw any graphs. now, try again

**live_laugh_luv27** · August 9th 2009, 10:29 AM

Originally Posted by Plato

What does any of the above have to do with the basic definitions of odd & even?
$\text{Odd functions are such that }f(-x)=-f(x)$

$\text{Even functions are such that }f(-x)=f(x)$

so these answers are incorrect?

- even

- odd

- even

**Jhevon** · August 9th 2009, 10:31 AM

Originally Posted by live_laugh_luv27

so these answers are incorrect?

- even

- odd

- even

yes, they are wrong. did you try what i said?

**live_laugh_luv27** · August 9th 2009, 10:33 AM

= $\sqrt{-x}$ = odd

= $2^{-x}$ = odd?

= $\frac{ln(-x )}{ln2}$ ?

**Jhevon** · August 9th 2009, 10:36 AM

Originally Posted by live_laugh_luv27

= $\sqrt{-x}$ = odd

?! are you telling me that, for example, $\sqrt 2 = \sqrt {-2}$ ? and if so, does that comply with the definition of an odd function as defined in my and Plato's posts?

= $2^{-x}$ = odd?

interesting. say $x = 1$ , is it true that $2^1 = 2^{-1}$ or $-2^1 = 2^{-1}$ ?

= $\frac{ln(-x )}{ln2}$ ?

tell me, what's $\log_2 (-5)$ , say

**live_laugh_luv27** · August 9th 2009, 10:52 AM

=

= $-\sqrt{x}$ = $-f(x)$ ?

is not true

is $\frac{ln(-5)}{ln(2)}$ ?

**Jhevon** · August 9th 2009, 10:57 AM

Originally Posted by live_laugh_luv27

=

= $-\sqrt{x}$ = $-f(x)$ ?

is not true

is $\frac{ln(-5)}{ln(2)}$ ?

ok, as far as real numbers are concerned, the square root function and the logarithm function are not defined for negative real numbers.... you should know this. please look this up and make sure you get it

and clearly $2^1 \ne 2^{-1}$ nor does $-2^1 = 2^{-1}$ so that $f(x) = 2^x$ is neither even nor odd.

Thread: even/odd graph

LinkBack

Thread Tools

Display

even/odd graph

Similar Math Help Forum Discussions

Graph Theory / Chromatic Number of a Complete Graph

Graph the equation of the translated graph in general form?

Graph Theory: Relationship between maximum degree of a graph and maximal matching

Graph Theory - Size of a Line Graph

Potential Energy Graph for a Reaction (can someone explain the graph please?)

Search Tags