How do you find the range of this problem?

Question

y = 4^x - 5

Where do I even look for the range?

Answer 1

We have to look at the 4^x term
if x> 0 , then 4^x is obviously positive.
if x= 0 then 4^0 = 1
for x < 0, we get 1/4^x which is 1/(positive number)

now for huge negative values of x, the denominator in
1/4^x becomes huge and 1/4^x approaches, but will never reach zero

so we have y > - 5 as the range.

Answer 2

So is that the "K" I'm looking at to solve for the range-my teacher keeps talking about the a h, k, ect and what effect they have

Like if it said y = 2^x + 8
the range would be y>6

Thank you

Answer 3

in your second example the range would be
y ≥ 8 , not 6

since 2^x > 0 for all x,
you are adding a positive value to 8, so you are looking at something > 8

Answer 4

Okay, let me try this again-I meant 8, not 6-a typo but then why is y>=8 in this one and the other one it is y>-5 and not greater and equal-is it because of the positive sign?

So for y = 3^x - 4, the range would be y >-4 and not y >= (-4), right-I'm just trying to really understand

Answer 5

You are right, it should be y > 8 , my typo.

and your last example is correct too.

It has to be > and not ≥ since the term 3^x can never really become zero, so you always adding something which is positive.

Answer 6

Thanks-much appreciated