Question

What is the range of the function?
y = x +3; -3 < x<4

Answer 1

To find the range of the function \( y = x + 3 \) for the interval \( -3 < x < 4 \), we first determine the minimum and maximum values of \( y \) when \( x \) is at the endpoints of the interval.

1. **Find the corresponding \( y \) values for the endpoints:**

- When \( x = -3 \):
\[
y = -3 + 3 = 0
\]

- When \( x = 4 \):
\[
y = 4 + 3 = 7
\]

2. **Determine the values of \( y \) based on the open interval**:

Since \( x \) is strictly between \(-3\) and \(4\) (i.e., \(-3 < x < 4\)), the corresponding \( y \) values will also be in the open range that excludes the endpoints:

- At the lower limit, \( x = -3 \) gives \( y = 0 \), but since \( x = -3 \) is not included, \( y \) will be greater than \( 0 \).

- At the upper limit, \( x = 4 \) gives \( y = 7 \), but since \( x = 4 \) is also not included, \( y \) will be less than \( 7 \).

3. **Conclusion**:

The range of the function \( y = x + 3 \) for the interval \( -3 < x < 4 \) is:

\[
(0, 7)
\]

Thus, the range of the function is \( (0, 7) \).