Explanation of Functions (1 Viewer)

[SnowFox]

Can someone right up an explanation of functions?

Like for example, the question y=x^2, and the answer in the back is all real positive and zero.

Explain how they got the answer, what real numbers are and anything else relevant to answer them.

 

[Timothy.Siu]

all real numbers just means "all" numbers. thats about all u need to know for 2unit.

is the question asking for range and domain?
range is y is greater than or equal to 0, this can be observed if u draw the parabola, because the vertex is at (0,0) and concave up, and hence y is greater than or = to 0

for the domain, x can be all real numbers as there are no restrictions on it.
restrictions can include square roots or an x being on the denominator of a fraction or something

 

[tommykins]

A function is strictly a 'machine' that provide a single unique output when you have an input.

A function f can be defined as f: R -> R, f(x) is a VALUE, NOT a function.

For example, in your case -

f: x->x^2
This can be expressed as f(x) = x^2
The domain of the function is whatever value of x we can use, so in our case we can use ALL values of x and still make it a function.
The range (or co-domain) is what the possible values of f(x) is. As you can see, x^2 is ALWAYS positive or 0, thus the codomain is 0<=

Formally
Domain(f) = (-infinity,infinity) or All
Range(f) = [0,infinity)

 

[SnowFox]

So what would y=(1/2)^x be?

 

[Timothy.Siu]

So what would y=(1/2)^x be?

yeah

 

[tommykins]

Dom(f) = All R x
Range(f) = [0,infinity)

 

[ForbiddenND]

A function is strictly a 'machine' that provide a single unique output when you have an input.

A function f can be defined as f: R -> R, f(x) is a VALUE, NOT a function.

For example, in your case -

f: x->x^2
This can be expressed as f(x) = x^2
The domain of the function is whatever value of x we can use, so in our case we can use ALL values of x and still make it a function.
The range (or co-domain) is what the possible values of f(x) is. As you can see, x^2 is ALWAYS positive or 0, thus the codomain is 0<=

Formally
Domain(f) = (-infinity,infinity) or All
Range(f) = [0,infinity)

i hate that machine analogy :S

 

[tommykins]

i hate that machine analogy :S

courtesy of John Steele

 

[Gibbatron]

Dom(f) = All R x
Range(f) = [0,infinity)

Not quite right, as anything to the power of 0, for example when y=(1/2)^0, is 1. Therefore the range is actually all real values >0, or in your form

Range(f)=positive infinity

 

[omniscience]

1+1 = 2 my friend

you can use this fundamental fact to solve pretty much anything like:

1+2 = 3
2+2 = 4
and so on...