Question
What is the range and domain of y=2/3x-4?
Answers
GPT-4o mini
To determine the domain and range of the function \( y = \frac{2}{3}x - 4 \), we can analyze the function based on its characteristics.
### Domain:
The domain of a function is all the possible values of \( x \) that can be input into the function. Since this is a linear function and there are no restrictions (such as division by zero or square roots of negative numbers), the domain is all real numbers.
**Domain:** \( (-\infty, \infty) \)
### Range:
To find the range, we consider the output values \( y \) that result from the domain of the function. As a linear function, it will also take all real values. Specifically, the slope of \( \frac{2}{3} \) indicates that as \( x \) increases or decreases, \( y \) will also increase or decrease without bound.
**Range:** \( (-\infty, \infty) \)
### Summary:
- **Domain:** \( (-\infty, \infty) \)
- **Range:** \( (-\infty, \infty) \)
### Domain:
The domain of a function is all the possible values of \( x \) that can be input into the function. Since this is a linear function and there are no restrictions (such as division by zero or square roots of negative numbers), the domain is all real numbers.
**Domain:** \( (-\infty, \infty) \)
### Range:
To find the range, we consider the output values \( y \) that result from the domain of the function. As a linear function, it will also take all real values. Specifically, the slope of \( \frac{2}{3} \) indicates that as \( x \) increases or decreases, \( y \) will also increase or decrease without bound.
**Range:** \( (-\infty, \infty) \)
### Summary:
- **Domain:** \( (-\infty, \infty) \)
- **Range:** \( (-\infty, \infty) \)