Question

y=2^-x-1
what is the domain, range and intercept of this function?

Answer 1

Is the function:
y = 2^(-x-1)

or
y = 2^(-x) - 1?

Answer 2

the second one

Answer 3

Let's simplify this then..
y = 1/ (2^x) - 1

I did this because fraction are very important to domains, we don't want zeros in fractions.

Here a graph of the function, for you to better follow in the analysis below:
http://www.wolframalpha.com/input/?i=plot+1%2F%282^x%29+-+1

Domain: This function is undefined everywhere where (2^x) = 0 Fortunately, if we do some graphical analysis, we can see that 2^x never actually touches 0
http://www.wolframalpha.com/input/?i=plot+2^x

it gets infinitely close to 0, but never touches it, so we're safe in saying that the domain of our function is all real numbers.

Range: All real numbers greater than -1.
Looking at our function, if we have a negative x our first term is no longer a fractions
IE f(-2) = 1/(2^-2) -1 = 2^2 -1 = 3. So all negative values of x give us positive numbers (if you don't believe me, try a few negative numbers).

Now what happens when x = 0. Well, we see that this function becomes:
f(0) = 1/2^0 - 1 = 1/1 - 1 = 0.

and then if we analyze all positive numbers, we see that that first term becomes a bigger and bigger fraction as the x values increase. This means that the "-1" will dominate the function. and create y values between -1 < y < 0. So, the lowest our graph can be is "-1" (this is actually could only ever happen at infinity, but we won't worry about that).

As for the intercepts, I would set y = 0 for the y -intercept of the function, and x = 0, for the x-intercept.

Answer 4

That makes sense, thanks!