Question
f(x) = x+7 underrrot find domain and range
Answers
GPT-4o mini
To find the domain and range of the function \( f(x) = x + 7 \), we first need to understand the nature of the function.
1. **Domain**: The domain of a function is the set of all possible input values (or x-values) for which the function is defined. The function \( f(x) = x + 7 \) is a linear function, which means it is defined for all real numbers. Therefore, the domain is:
\[
\text{Domain: } (-\infty, \infty)
\]
2. **Range**: The range of a function is the set of all possible output values (or y-values) that the function can produce. Since \( f(x) = x + 7 \) is also a linear function with a slope of 1 (which means it increases without bound), it can also produce every real number as an output. Thus, the range is:
\[
\text{Range: } (-\infty, \infty)
\]
In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( (-\infty, \infty) \)
1. **Domain**: The domain of a function is the set of all possible input values (or x-values) for which the function is defined. The function \( f(x) = x + 7 \) is a linear function, which means it is defined for all real numbers. Therefore, the domain is:
\[
\text{Domain: } (-\infty, \infty)
\]
2. **Range**: The range of a function is the set of all possible output values (or y-values) that the function can produce. Since \( f(x) = x + 7 \) is also a linear function with a slope of 1 (which means it increases without bound), it can also produce every real number as an output. Thus, the range is:
\[
\text{Range: } (-\infty, \infty)
\]
In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( (-\infty, \infty) \)