Question
What are the domain and range of this function?
y=|x–3|
y=|x–3|
Answers
GPT-4o mini
To determine the domain and range of the function \( y = |x - 3| \), we can analyze its characteristics:
**Domain:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
For the absolute value function \( |x - 3| \), there are no restrictions on the values of \( x \). Therefore, the domain of the function is:
\[
\text{Domain: } (-\infty, \infty)
\]
**Range:**
The range of a function is the set of all possible output values (y-values) that the function can produce.
The function \( y = |x - 3| \) represents the distance of \( x \) from 3, which is always non-negative. The minimum value occurs when \( x = 3 \), giving \( y = |3 - 3| = 0 \). As \( x \) moves away from 3 in either direction, \( y \) increases without bound.
Therefore, the range of the function is:
\[
\text{Range: } [0, \infty)
\]
In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( [0, \infty) \)
**Domain:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
For the absolute value function \( |x - 3| \), there are no restrictions on the values of \( x \). Therefore, the domain of the function is:
\[
\text{Domain: } (-\infty, \infty)
\]
**Range:**
The range of a function is the set of all possible output values (y-values) that the function can produce.
The function \( y = |x - 3| \) represents the distance of \( x \) from 3, which is always non-negative. The minimum value occurs when \( x = 3 \), giving \( y = |3 - 3| = 0 \). As \( x \) moves away from 3 in either direction, \( y \) increases without bound.
Therefore, the range of the function is:
\[
\text{Range: } [0, \infty)
\]
In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( [0, \infty) \)