Determine if the relation y=4x−1 is a function by first graphing the relation, then applying the vertical line test. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.(1 point)
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.
are you sure
Yes, I am sure that the relation y=4x-1 is a function. The graph of the equation is a straight line, and it passes the vertical line test. This means that for every x-value, there is only one corresponding y-value, indicating that the relation is a function.
To determine if the relation y = 4x - 1 is a function, you can follow these steps:
1. Graph the relation:
- Choose a range of x-values, for example, -5 to 5.
- Substitute each x-value into the equation y = 4x - 1 to find the corresponding y-values.
- Plot the points (x, y) on a graph.
- Connect the points to form a line.
2. Apply the vertical line test:
- Imagine a vertical line moving from left to right across the graph.
- If the vertical line intersects the graph at more than one point at any given x-value, then the relation is not a function.
- If the vertical line intersects the graph at most one point for every x-value, then the relation is a function.
3. Determine if the relation is a function:
- Analyze the graph and observe if any vertical lines intersect more than once.
- If you find any vertical lines that intersect the graph at more than one point, then the relation is not a function.
- If every vertical line intersects the graph at most one point, then the relation is a function.
Therefore, by graphing the relation y = 4x -1 and applying the vertical line test, you can determine if the relation is a function or not.