Question

y=-1/2(x+2)(x+2)-1

Answer 1

what is the instruction? find x in terms of y? factor?

Answer 2

y = (1/2)^x
is an exponential function where x is the exponent

1° case when x approaches negative infinity
Note that y = (1/2)^x = 2^(-x) so when x -> (-inf.), function approaches y = 2^[-(-inf)] = 2^(+inf)
and lim(y) {x -> -inf} = +inf
When x decreases to -inf., y grows to +inf

2° case when x approaches positive infinity
We can write
y = (1/2)^x = f(x)/g(x)
where f(x)=1 and g(x)=2^x
and then use following rule
lim[f(x)/g(x)] {x -> inf} = lim f(x) {x -> inf} / lim g(x) {x -> inf}
therefore
lim[(1/2)^x] {x -> inf} = lim[1/(2^x)] {x -> inf} = lim (1){x -> inf} / lim (2^x){x -> inf}
lim (1){x -> inf} = 1
lim (2^x){x -> inf} = inf
lim[(1/2)^x] {x -> inf} = 1 / inf. = 0
The limit of y as x approaches +infinity is 0.
That means horizontal line y=0 is horizontal asymptote of function y = (1/2)^x.

3° intercept with y-axis
For x=0,
y = (1/2)^0 = 1

Answer 3

holy geez man.

Answer 4

yeah, just cover every possibly question right

Answer 5

well...at least he's precise nottim =)) the asker may just choose which answer he desires

Answer 6

clarencema, when you're done reading, do you have what you need?

Answer 7

NotTim would be willing to add information? /:) i think he pretty much covered every possibility haha :))