Is the Evenness of a Function Related to its Limits?

[Jan Hill]

Homework Statement

Suupose that f(x) is an even function of x. Does knowing that lim as x approaches 2 from the left of f(x) = 7 tell anything about either limit of f(x) as x approaches -2 from the left or the limit of f(x) as x approaches -2 from the right?

Homework Equations

The Attempt at a Solution

This must have something to do with the 'even' characterisitic of the function. However, doesn't being odd or even when considering functions just mean whether or not the powers of the x's in the function add up to an even or odd number. Does 'eveness' mean something like the function is reflected across the y-axis and something critical follows from this?

 

[╔(σ_σ)╝]

Even functions are symmetric across the y axis, that is, f(-x)=f(x).

So what do you think ?

 

[arkajad]

http://en.wikipedia.org/wiki/Even_function#Even_functions"

 

[HallsofIvy]

Homework Statement

Suupose that f(x) is an even function of x. Does knowing that lim as x approaches 2 from the left of f(x) = 7 tell anything about either limit of f(x) as x approaches -2 from the left or the limit of f(x) as x approaches -2 from the right?

Homework Equations

The Attempt at a Solution

This must have something to do with the 'even' characterisitic of the function. However, doesn't being odd or even when considering functions just mean whether or not the powers of the x's in the function add up to an even or odd number. Does 'eveness' mean something like the function is reflected across the y-axis and something critical follows from this?

"Reflecting" about the y-axis maps 1 and 2 into -1 and -2. Approaching 2 "from the left" (from the direction of 1) reflects into "approaching -2 from the direction of -1" and so into "approaching -2 from the right".

 

[Jan Hill]

So we can say that the function is reflected about the y-axis and that therefore f(X) = 7 for the limit as x -->-2from the left or right, right?