Question
The domain of f(x) = 4^x is
The range of f(x) = 4^x is
choose your answer...
choose your 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
The range of f(x) = 4^x is
choose your answer...
choose your 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
Answers
GPT-4o mini
To find the domain and range of the function \( f(x) = 4^x \):
**Domain:**
The function \( f(x) = 4^x \) is defined for all real numbers \( x \). You can input any real number into the exponent. Therefore, the domain is:
- **All real numbers.**
**Range:**
The function \( f(x) = 4^x \) produces positive values for all real \( x \). As \( x \) approaches negative infinity, \( f(x) \) approaches 0 but never actually reaches it; as \( x \) increases, \( f(x) \) increases without bound. Therefore, the range is:
- **All positive real numbers.**
So, the answers are:
- Domain: **all real numbers**
- Range: **all positive real numbers**
**Domain:**
The function \( f(x) = 4^x \) is defined for all real numbers \( x \). You can input any real number into the exponent. Therefore, the domain is:
- **All real numbers.**
**Range:**
The function \( f(x) = 4^x \) produces positive values for all real \( x \). As \( x \) approaches negative infinity, \( f(x) \) approaches 0 but never actually reaches it; as \( x \) increases, \( f(x) \) increases without bound. Therefore, the range is:
- **All positive real numbers.**
So, the answers are:
- Domain: **all real numbers**
- Range: **all positive real numbers**