MEDAL!!!

How to find the domain and range of
$f(x) = 3(x - 4)^2 - 6$

Question

MEDAL!!!


How to find the domain and range of 
$f(x) = 3(x - 4)^2 - 6$

anonymous · Answer

you do not find the domain, you are supposed to be told the domain
but since this is a polynomial, the natural domain is all real numbers

calculusxy · Answer

Would the domain be $\mathbb{R}$

anonymous · Answer

yes it would

alexandervonhumboldt2 · Answer

yes

calculusxy · Answer

It took me forever to get that real sign

calculusxy · Answer

Anyway, thanks!

anonymous · Answer

$$\mathbb{R}$$

anonymous · Answer

$$\mathbb{C}$$

anonymous · Answer

just showing off
 it is \mathbb{R}

anonymous · Answer

you got the range?

calculusxy · Answer

would the range be $\mathbb{R}$ as well?

anonymous · Answer

oh no

anonymous · Answer

it is a parabola that opens up

anonymous · Answer

in particular $$(x-4)^2\geq 0$$ since it is a square 
so therefore $$3(x-4)^2\geq 0$$ as well

anonymous · Answer

that makes $$3(x-4)^2-6\geq -6$$ the range is $$[-6,\infty)$$

anonymous · Answer

your quadratic is in vertex form, the vertex is $(4,-6)$ so it goes from $-6$ up

calculusxy · Answer

I don't understand @satellite73

calculusxy · Answer

@jim_thompson5910

jim_thompson5910 · Answer

|dw:1448935604099:dw|

jim_thompson5910 · Answer

The best way to find the range is to picture the graph of f(x)

it looks something like this (it's just a rough sketch)

|dw:1448935673827:dw|

some parabola that opens upward. The leading coefficient a = 3 is positive, meaning that the parabola opens upward

jim_thompson5910 · Answer

the lowest point is the vertex which in this case is (4,-6)

|dw:1448935724216:dw|