Question

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Answer 1

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

Answer 2

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]

Answer 3

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

Answer 4

x is all read numbers

Answer 5

lol

Answer 6

that d was suppose to be an l

Answer 7

lol

Answer 8

thats so funny

Answer 9

its not that funny :)

Answer 10

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

Answer 11

calculus way is funner

Answer 12

And easier!

Answer 13

yep

Answer 14

i don't understand how you guys got that answer

Answer 15

the one with the weird symbol?

Answer 16

yup

Answer 17

this symbol ' ?

Answer 18

don't worry about that way

Answer 19

We got it with Calculus!

Answer 20

ohhhhh. good thing i didn't write that down

Answer 21

lol

Answer 22

will you take cal?

Answer 23

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

Answer 24

you will find that calculus is more fun than algebra

Answer 25

You CAN write it down. Impress your teachers!!

Answer 26

;)

Answer 27

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.

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

Because the leading coefficient is positive.

Answer 34

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?

Answer 35

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

Answer 36

that probably didn't make much sense..

Answer 37

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.

Answer 38

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

Answer 39

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.