Question

9. Graph the function f on a coordinate grid
x f(x)
0 < x <= 1 4
1 < x <= 2 5
2 < x <= 3 6
3 < x <= 4 7
4 < x <= 5 8
5 < x <= 6 9

Answer 1

To graph f, plot six horizontal line segments on the intervals (0,1], (1,2], (2,3], (3,4], (4,5], (5,6] at the given constant y-values. Each segment has an open circle at its left endpoint and a closed (filled) dot at its right endpoint because the left inequality is strict (>) and the right inequality is ≤.

Segments and endpoints:
- On (0,1]: y = 4. Open at (0,4), closed at (1,4).
- On (1,2]: y = 5. Open at (1,5), closed at (2,5).
- On (2,3]: y = 6. Open at (2,6), closed at (3,6).
- On (3,4]: y = 7. Open at (3,7), closed at (4,7).
- On (4,5]: y = 8. Open at (4,8), closed at (5,8).
- On (5,6]: y = 9. Open at (5,9), closed at (6,9).

Domain: (0,6]. For x ≤ 0 or x > 6 the function is not defined.

Label the x-axis 0 through 6 and the y-axis at least 4 through 9, draw the horizontal segments at the listed y-values, and mark the open/closed endpoints as described.