HELP ME PLEASE the function f is defined as follows f(x)=4+x if x or equal to 0 A) find the domain of the function B) Locate any intercepts C) Graph the function D) based on the graph, find the range E) is f continuous on its domain?

Question

HELP ME PLEASE 
the function f is defined as follows
f(x)=4+x if x < 0
        x^2 if x >or equal to 0

A) find the domain of the function
B) Locate any intercepts
C) Graph the function
D) based on the graph, find the range
E) is f continuous on its domain?

blurbendy · Answer

f(x) = x^2 if x >= to 0?

anonymous · Answer

yes

blurbendy · Answer

The domain of the first one would be all negative numbers to infinity, because x has to be < 0.  Can you figure out the domain of f(x) = x^2 if x >= 0 ?

anonymous · Answer

wouldn't that be (0, infinity)
so would the domain be (-infinity, infinity)

blurbendy · Answer

it would need to be [0, infinity), you need the bracket because x is greater than or EQUAL to 0.  if it can equal 0, then you have to include it in the domain, and you do that by using [

sidenote: infinity never has has a [

anonymous · Answer

so the domain would be [0, infinity) what about the other equation?

blurbendy · Answer

the domain of f(x) = x^2 is [0, infinity)

anonymous · Answer

yes but the overall domain would be (-infinity, infinity) right?

blurbendy · Answer

the domain of the first one is (0, -infinity)

blurbendy · Answer

you dont include 0 this time

anonymous · Answer

so the overall equation for both domain would be (-infinity, 0) U [0, infinity) ??

blurbendy · Answer

yes!!

anonymous · Answer

then what would be the range???

blurbendy · Answer

so what would happen if you started plugging in negative numbers for x in the first equation?  what's the first answer you would get

anonymous · Answer

the out come would be neg.

blurbendy · Answer

4 + (-1) = 3
4 + (-2) = 2
4 + (-infinity) = -infinity
so what's the range?

anonymous · Answer

range would be (-infinity, infinity)...??

blurbendy · Answer

(-infinity, 3] for the first one

blurbendy · Answer

what about the second?

anonymous · Answer

wouldn't it be (-infinity , 4)
second would be [o, infinity)

blurbendy · Answer

you can write it either way

blurbendy · Answer

and yes, that is the second one

anonymous · Answer

then the interception would be (0,4) and [0,0]

blurbendy · Answer

have you graphed the function?

anonymous · Answer

yes the first equation y intercept is 4 but its an open circle, also have a x intercept of [-4,0] and the second equation stats at (0,0) and continues to infinity

for got about the x intercept on the first intercept

blurbendy · Answer

(0,0) and (1,1)
f(-4) = 4  + (-4) = 0
f(0) = (0)^2 = 0

f(3) = 4 + (-3) = 1
f(1) = x^2 = 1

anonymous · Answer

so would it be [0,0] and [-4,0] then why (1,1)

blurbendy · Answer

intercepts are ordered pairs, you write them like this ( x , y )
the only places they intersect are (0,0) and (1,1)

blurbendy · Answer

look at why that is two posts up

anonymous · Answer

but they don't intercept at (0,0) or (1,1) on the grpah

blurbendy · Answer

i just graphed it in my calculator.  they dont intersect at whole numbers actually...

blurbendy · Answer

wait, there are constraints

blurbendy · Answer

there arent any intercepts.

blurbendy · Answer

because the functions are constrained

anonymous · Answer

i think the intercept would be any intercept on the y axis and the x axis
and yes there are constrains next to the equation would the constrained

blurbendy · Answer

intercepts are where the two equations equal the same thing given the SAME input.  This can never occur because the functions are constrained

anonymous · Answer

|dw:1361731062528:dw| is somewhat how the graph looks like