Question
Find the domain and range of the function.
yequals8xplus7
yequals8xplus7
Answers
GPT-4o mini
To find the domain and range of the function \( y = 8x + 7 \), we analyze it as follows:
### Domain
The domain of a function is the set of all possible input values (i.e., \( x \)-values) for which the function is defined. Since \( y = 8x + 7 \) is a linear function, there are no restrictions on the value of \( x \). Therefore, the domain is:
\[
\text{Domain} = (-\infty, \infty)
\]
### Range
The range of a function is the set of all possible output values (i.e., \( y \)-values). Since the equation \( y = 8x + 7 \) is a linear equation with a non-zero slope (which is 8), it will produce every real number as \( x \) varies from \( -\infty \) to \( \infty \). Thus, the range is also:
\[
\text{Range} = (-\infty, \infty)
\]
### Conclusion
The domain and range of the function \( y = 8x + 7 \) are:
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( (-\infty, \infty) \)
### Domain
The domain of a function is the set of all possible input values (i.e., \( x \)-values) for which the function is defined. Since \( y = 8x + 7 \) is a linear function, there are no restrictions on the value of \( x \). Therefore, the domain is:
\[
\text{Domain} = (-\infty, \infty)
\]
### Range
The range of a function is the set of all possible output values (i.e., \( y \)-values). Since the equation \( y = 8x + 7 \) is a linear equation with a non-zero slope (which is 8), it will produce every real number as \( x \) varies from \( -\infty \) to \( \infty \). Thus, the range is also:
\[
\text{Range} = (-\infty, \infty)
\]
### Conclusion
The domain and range of the function \( y = 8x + 7 \) are:
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( (-\infty, \infty) \)