Determining range, HELP!?

Question

What is the range of y = 5(2)^x - 4?

is it:

*The set of positive real numbers greater than 0
*The set of positive real numbers greater than -4
*The set of positive real numbers greater than 1
*The set of positive real numbers greater than 4

Answer 1

Exponential equations (y=n^x) have a range of (0,infinity) with an asymotote at y=0. This equation is shifted down 4 so the range is also shifted down 4 and becomes (-4,infinity)

Answer 2

range is (-4, inf)
different ways to do it;

start with the graph & range of 2^x:
range is (0, inf)
so graph of 5 (2^x) is stretched by factor of 5,
range is still (0, inf)
so graph of 5 (2^x) -4 is moved down by 4,
so range is now (-4, inf)

or

when is y big? any time x is big. so your 'upper bound' is infinity.
when is y small? well, the smaller x gets, the smaller y gets.
what is the smallest y could be? well, if x was some hugely negative number, like -1000000, then 2^x would be almost zero, so 5 (2^x) would be almost zero, so 5 (2^x) - 4 would be almost zero minus four. which is almost -4. But since you never get quite to zero, your interval is open instead of closed.
Therefore: (-4, inf)

Answer 3

What is the range of y = 5(2)^x - 4?
-4

Answer 4

I would say > -4
Since 5*2^x would get closer to zero without hitting zero as x got further negative.