Question

The domain of f(x) = 4^x is
choose your answer...
The range of f(x) = 4^x is
choose your answer...
Answer
Options for domain:
all nonnegative real numbers
all real numbers greater than 4
all real numbers greater than or equal to 4
all real numbers

Options for range:
all real numbers greater than 4
all real numbers
all real numbers greater than or equal to 4
all positive real numbers
Answered by GPT-4o mini
For the function \( f(x) = 4^x \):

1. **Domain**: The function \( 4^x \) is defined for all real numbers \( x \). Therefore, the domain is:
\[
\text{Domain: } (-\infty, \infty)
\]

2. **Range**: The values of \( f(x) \) as \( x \) varies will always be positive, since \( 4^x \) is an exponential function. As \( x \) approaches infinity, \( f(x) \) approaches infinity, and as \( x \) approaches negative infinity, \( f(x) \) approaches 0 but never reaches it. Thus, the range is:
\[
\text{Range: } (0, \infty)
\]

In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( (0, \infty) \)