Graph of function f of x equals 2 to the power of negative x. Graph of function g of x equals 5 to the power of x. Graph of p of x is a line segment connecting points negative 1, negative 3 and 2, 12.
Which function has all real numbers as its domain?
Only f(x)
Both g(x) and p(x)
Both f(x) and g(x)
Only p(x)

- anonymous

- chestercat

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- anonymous

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- anonymous

will give medal for right answer

- geerky42

What do you think?
Can you plug -2 in p(x)?

- anonymous

yeah u can ? i think

- geerky42

ok what is p(-2)?

- anonymous

-2p

- geerky42

Domain is basically "group" of x-coordinates.
Do p(x) have value in x=-2 ?

- geerky42

p(x) is function, not variable

- anonymous

i am like very bad at math lol but i think it dont

- geerky42

let's just say you have h(x) = x
h(x) has domain of all real number because you can plug any values in h(x)

- anonymous

okay

- geerky42

You can see that p(x) only goes from about -1 to 2 in x-coordinate, right?

- anonymous

yes i do

- geerky42

|dw:1438987265095:dw|

- anonymous

|dw:1438987281477:dw|

- geerky42

yeah there are ends.
So domain of p(x) is not all real number. Does that make sense?

- anonymous

yes it do

- geerky42

p(-3) is not definied (has no value) because -3 is not in domain of p(x)

- geerky42

okay what about f(x) and g(x)?

- geerky42

defined *

- anonymous

|dw:1438987402176:dw|

- geerky42

\(f(x) = 2^{-x}\)
\(g(x)=5^x\)
Is there any x value you cannot plug in?

- anonymous

-2

- anonymous

and 1 ?

- geerky42

f(-2) has no value?

- geerky42

well f(-2) = \(2^{-(-2)} = 2^2 = 4\)
So -2 is in domain of f(x). same goes for g(x)

- anonymous

okay i was right with the -2

- geerky42

well domain is more than just -2.

- geerky42

does f(10) have value?
f(100)?
f(1000)?

- anonymous

100

- geerky42

and not f(10) nor f(1000)?

- geerky42

Looks like you don't understand how functions work.

- anonymous

i dont

- geerky42

you can think of it as "machine"|dw:1438987847196:dw|
like f(x) would "change" -2 to any number, depend on what f(x) is.
Make sense so far?

- anonymous

okay i see what u mean

- geerky42

domain is basically like what number you can put into machine

- geerky42

if domain is 1 to 3, you can only put in any number between 1 to 3. No 5 or something

- geerky42

If domain is real number, that means you can put in ANY (real) number.

- anonymous

okay

- geerky42

do you understand?

- anonymous

so i can say any number

- geerky42

well, can you plug any number in f(x) and g(x)? That's the question

- anonymous

yes u can

- geerky42

ok so domain of f(x) and g(x) is real number.

- anonymous

yes

- geerky42

So answer is C.

- geerky42

sorry for taking so long time lol

- anonymous

thxs for trying to show me i really do want to learn math

- geerky42

Glad to hear that!

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