Functions and Graphs (1 Viewer)

[Chelsea FC]

Can someone explain this Odd and Even function and Domain and Range. This is so fuking difficult for me, Im doing it at James An Coaching College.

Its in Maths in Focus (2unit, Preliminary) on page 170-183.

 

[jb_nc]

Odd: -ƒ(x) = ƒ(-x)
Even: ƒ(x) = ƒ(-x)

Examples:

Even: x², x^4, cos x
Odd: sin x, tan x, x, x³.

Try for ƒ(x) = x²
ƒ(-x) = (-x)² = x²

Domain and range:
The [natural] domain of a function is the set of all numbers for which the formula makes sense - that is, the set of all possible inputs.

The range of a function is the set of corresponding outputs - that is, the set of all values of f(x) as x runs through all values in the domain.

Examples:
(a) What is the domain of the function given by g(x) = (3x² - 1)/(x - 2)?

g(x) is an example of a rational function and is define of all values of x except those which makes the denominator equal to zero. The domain of g is therefore {x ∈ R | x =/= 2} or (-∞, 2) U (2, ∞).

(R in this case means all real numbers, just fyi).

I'll do another with range and a harder function:
(b) Find the natural domain and range of f(x) = ln (cos² x)

If f(x) = ln (cos² x) then f has the domain:

{x ∈ R | cos² x > 0} = {x ∈ R| x =/= ±π/2, ±3π/2, ±5π/2...}

Corresponding range is (-∞, 0] as cos² x takes all values in the interval (0, 1].

That took a long time to type out. Hope this helps.

 

[watatank]

Additional information:

The graph of an even function will reflect off the y axis (think of parabola)

The graph of an odd function will reflect off the y axis and rotate 180* (think cubic)

Domain: all values for x where the function holds true

Range: all values for y where the function holds true

Hope that helps :wave:

 

[Laura_123]

A function is EVEN if its' axis of symetry is the y axiz. Like you can reflect it exactly onto tho other side.

A function is ODD if you can rotate it around the origin and you get the SAME graph before you go the whole 36o degrees.

Just as Watatank said-parabola (y = x squared) for even, cubic (y = x cubed)for odd. DON'T just think an odd function is not reflected over the other side.

Domain is all the x vaulues you can use, and is quite often just all numbers in the real number system.
Range is all the numbers you can get. You may have to use the axis of symatery to get this alot of the time.

Good luck :wave: