Question

What are the domain and range of the function f(x) = 2^x+1?

Answer 1

Answer:

Domain: (-∞, ∞)

 Range: (0,∞)

Step-by-step explanation:

Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis unless a value has been added to it. If it has, the curve shifts. This function has addition on the exponent but not to the whole function so it does not change the asymptote. Its y - values remain between 0 and ∞. This is the range, the set of y values.

However, the range of exponentials can change based on the leading coefficient. If it is negative the graph flips upside down and its range goes to -∞. This doesn't have it either.

The addition to 1 on the exponent shifts the function to the left but doesn't change the range.

In exponential functions, the x values are usually not affected and all are included in the function. Even though it shifts, the domain doesn't change either. Its domain is (-∞, ∞).

Domain: (-∞, ∞)

 Range: (0,∞)