To graph the relation y=4x-1, we can start by plotting a few points.
Let's choose x-values of -2, -1, 0, 1, and 2:
When x = -2, y = 4(-2) - 1 = -9
When x = -1, y = 4(-1) - 1 = -5
When x = 0, y = 4(0) - 1 = -1
When x = 1, y = 4(1) - 1 = 3
When x = 2, y = 4(2) - 1 = 7
The points we have plotted are (-2, -9), (-1, -5), (0, -1), (1, 3), and (2, 7).
Now, if we graph these points, we can see that they form a straight line:
-9 |
-5 |
-1 |
3 |
7 ────────────────
-2 -1 0 1 2
This graph shows that for every x-value, there is a unique y-value. There are no vertical lines that intersect the graph at more than one point. Therefore, the relation y=4x-1 is a function.
So we would enter 1 to indicate that the relation is a function.