Question

what is the range of an exponential parent function with the base 2

Answer 1

The exponential parent function with base two is
f(x)=2^x
where x∈(-inf,inf).
when x-> -inf, f(x)-> 0
similarly, when x-> inf, f(x)-> inf
so the range of f(x) is (0,+inf).

Answer 2

Answer:

R = (0, +∞)

Step-by-step explanation:

The exponential parent function with base 2 is defined by the function

$f(x)=2^{x}$

The range is the set of all the values that the function f can have.

With the given function it is impossible to obtain negative results, that is, any number that has the variable x, whether positive or negative, results in the function f a number greater than zero.

So as x decreases towards -∞, the value of f becomes smaller with a tendency to zero (excluding zero).

$f(x)=2^{-inf}=\frac{1}{2^{inf}}=\frac{1}{inf}$ --> 0

But as x increases towards +∞, the function f becomes larger with a tendency to +∞.

$f(x)=2^{inf}$--> +∞

In conclusion, the range of the exponential parent function with base 2 is

R = (0, +∞)

Hope this hepls!