Mathematics
OpenStudy (anonymous):

:/

OpenStudy (anonymous):

y=x^2+6x+1 find the domain and range.

myininaya (myininaya):

all read numbers and i will give you a hint for the range i would write f in vertex form and also we know the function f is concave up so we have the range is [the y part of the vertex, infinity]

OpenStudy (anonymous):

x is all real numbers f(x)>-8

OpenStudy (anonymous):

myininaya (myininaya):

lol

myininaya (myininaya):

that d was suppose to be an l

OpenStudy (anonymous):

lol

myininaya (myininaya):

thats so funny

OpenStudy (anonymous):

its not that funny :)

OpenStudy (anonymous):

$f(x) = x^2+6x+1$$f'(x) = 2x + 6$ $f'(x) = 0$$2x + 6 = 0$$x = -3$ $f(-3) = (-3)^2 + 6(-3) + 1 = -8$ Range: $$[-8, \infty)$$

myininaya (myininaya):

calculus way is funner

OpenStudy (anonymous):

And easier!

myininaya (myininaya):

yep

OpenStudy (anonymous):

i don't understand how you guys got that answer

myininaya (myininaya):

the one with the weird symbol?

OpenStudy (anonymous):

yup

myininaya (myininaya):

this symbol ' ?

myininaya (myininaya):

OpenStudy (anonymous):

We got it with Calculus!

OpenStudy (anonymous):

ohhhhh. good thing i didn't write that down

myininaya (myininaya):

lol

myininaya (myininaya):

will you take cal?

OpenStudy (anonymous):

when I'm a junior in high school I will.

myininaya (myininaya):

you will find that calculus is more fun than algebra

OpenStudy (anonymous):

You CAN write it down. Impress your teachers!!

OpenStudy (anonymous):

;)

OpenStudy (anonymous):

For algebra you just have to see that it's a parabola opening upwards, so the minimum value will be the vertex. So find the vertex, and the range will be $$[y_1, \infty)$$ where $$y_1$$ is the y value of the vertex.

OpenStudy (anonymous):

hopefully it will be more fun. and hahaha, my teacher would probably freak out.

myininaya (myininaya):

no what would be more impressive if you actually used the formal definition of derivative

OpenStudy (anonymous):

but how do you know that it's a parabola pointing upwards in the first place?

OpenStudy (anonymous):

Well I think writing it down without understanding it will only impress upon h(is/er) teacher that (s)he cheated.

myininaya (myininaya):

f=x^2 is concave up f=-x^2 is concave down

OpenStudy (anonymous):

Because the leading coefficient is positive.

OpenStudy (anonymous):

ok. and i also have to graph this, and i get how to tell if its upwards/downwards now, but how do i know how wide the arc is?

myininaya (myininaya):

f=cx^2 c>0=> concave up c<0=> concave down

OpenStudy (anonymous):

that probably didn't make much sense..

OpenStudy (anonymous):

Well you can solve it for some y value (say y=0) and then you'll get two x values. That'll give you a decent approximation for a sketch.

OpenStudy (anonymous):

ok. and another question is $y=3(2)^{x}$ can I just plug in 0 as the x exponent?

OpenStudy (anonymous):

What you are really looking at is the limiting behaviour of the function. It is because the leading term dominates the other terms as $$x$$ approaches infinity that you are worried about the sign of its coefficient.