Q:

# Choose the best graph to match the given expression. F(x) = 2[x]

Accepted Solution

A:
1) The function [x] takes as input a real number x and gives as output the greatest integer less than or equal to x.

2) For example

[2] = 2
[2.1] =2
[2.8] = 2
[2.9999] = 2

[3] =3
[3.5] = 3
[3.999999] = 3

[4] = 4

3) So, 2 [x] will scale all the values of [x] by a factor of 2:

This is the result:

input               [x]           2[x]

- 8 ≤ x < - 7          -8            -16
- 7 ≤ x < - 6          -7            -14
- 6 ≤ x < - 5          -6            -12
- 5 ≤ x < - 4          -5            -10
- 4 ≤ x < - 3          -4            - 8
- 3 ≤ x < - 2          -3            - 6
- 2 ≤ x < - 1          -2            - 4
- 1 ≤ x < 0            -1            - 2
0 ≤ x < 1               0               0
1 ≤ x < 2               1               2
2 ≤ x < 3               2               4
3 ≤ x < 4               3               6
4 ≤ x < 5               4               8
5 ≤ x < 6               5             10
6 ≤ x < 7               6             12
7 ≤ x < 8               7             14
8 ≤ x < 9               8             16

4) You can see the graph of such function in the figure attached.

Take into account that the integer number to the right extreme of each segment is not included in the segment, but the left extreme is included.