Question

Which of the following functions have a domain of (-infinity, infinity) and a range of (5, infinity) ? (check all that apply)

A) f(x)=3^x + 5
B) f(x)= 3^x - 5
C) f(x)= 0.25^x + 5
D) f(x)= 0.25^x - 5

Answer 1

Domain is values that x can exist..
Range is the values that y can exist. (Or in this case f(x))

So this is sort of a graphing problem. If you're allowed to plug into a graphing calculator, it's easier.

Domain is always the easiest to figure out. What you're looking for are values of exist to where there is no solution. (For example, dividing by zero). Any number you can think of for x, all four solutions are valid, (including infinity)

Range: We need to think about where f(x) can and cannot exist.
For A)
If x is very very small, the 3^x goes to zero. Thus F(x) goes to 5. (lower bound)
If x is very very large, the 3^x is also large. Thus f(x) goes to infinity. (Upper Bound)

for B) Apply the same thing
If x becomes very very small, 3^x goes to zero, thus f(x) goes to -5. Which isn't in the bound, so that one doesn't work...

Now you just need to check C) and D)