Question

1. what is the domain of the function $y = 2^x$?

a. $x > 0$

b. $x < 0$

c. $(-\infty, \infty)$

d. $(0, \infty)$

Explanation:

Step1: Recall the domain of exponential functions

The general form of an exponential function is \( y = a^x \), where \( a>0 \) and \( a
eq1 \). For any real number \( x \), \( a^x \) is defined.

Step2: Analyze the given function \( y = 2^x \)

Here, \( a = 2 \) which satisfies \( a>0 \) and \( a
eq1 \). So, the input \( x \) can be any real number, which means the domain is all real numbers, or in interval notation \( (-\infty,\infty) \).

Answer:

c. \((-\infty, \infty)\)