Question

Find the Domain and Range of the function: g(x) = 200(2.06)x

Answer 1

@John_ES

Answer 2

Do yo mean,
\[y=200\cdot2.06^x\]?

Answer 3

Yes.

Answer 4

Domain are all reals, because exponential functions don't have any irregular points. Range is,
\[R=(0,+\infty)\]

Answer 5

Well it's a function so \[f(x) = 200(2.06)^{2}\]But: \[y = 200(2.06)^{2}\]is the same thing.

Answer 6

Yes, but where you put a 2 there should be a x, if not, the function would be a constant function.

Answer 7

But how would I write the Domain?

Answer 8

Right, sorry, I was kind of mixed up.

Answer 9

\[D=\mathbb{R}\]

Answer 10

Isn't it supposed to be written like ? ≤ x ≤ ?

Answer 11

And the range: ? ≤ y ≤ ?

Answer 12

So range = 0 ≤ y ≤ ∞

Answer 13

@John_ES

Answer 14

Range,
\[0<y\]

Answer 15

My lesson writes it in a different way.

Answer 16

to do this problem, we start with
\[ g(x) = 200(2.06)^x \]
for the domain, you start by assuming x goes from -infinity to + infinity
then you look to see if you would either
(1) divide by 0
(2) take the square root of a negative number.

Neither of those things can happen, no matter what value x is, so the domain is
\[ - \infty < x < \infty\]

Answer 17

Oh, thanks, that's how my lesson described it too.

Answer 18

to find the range, test a few values of x. If x is a very negative number
\[ g( -10000) = 200(2.06)^{-10000} =\frac{200}{2.06^{10000}} \]
200 divided by a very big number is close to 0... notice we never get to zero, but we can get very close. so the range is 0 < y
do the same thing for large x and we see y approaches + infinity

the total range is
0 < y < infinity

Answer 19

Ohh, thanks so much.

Answer 20

And what about,
\[g(100000000)=200\cdot(2.06)^{100000000}\]
Range must be y>0. The function diverges when x grew.