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.
We first graph the relation y=4x−1 by making a table of values and plotting the points:
| x | y |
|---|---|
| -3 | -13 |
| -2 | -9 |
| -1 | -5 |
| 0 | -1 |
| 1 | 3 |
| 2 | 7 |
| 3 | 11 |
The graph looks like:
We can now apply the vertical line test: if any vertical line intersects the graph at more than one point, then the relation is not a function. If every vertical line intersects the graph at most once, then the relation is a function.
In this case, we see that every vertical line intersects the graph at most once, so the relation is a function. Therefore, we enter 1.
To determine if the relation y = 4x - 1 is a function, we will first graph the relation and then apply the vertical line test.
To graph the relation, we need to see how the y-values change with respect to the x-values.
Step 1: Choose a set of x-values to plot on a graph. Let's choose x = -2, -1, 0, 1, and 2.
When x = -2, y = 4(-2) - 1 = -8 - 1 = -9.
When x = -1, y = 4(-1) - 1 = -4 - 1 = -5.
When x = 0, y = 4(0) - 1 = 0 - 1 = -1.
When x = 1, y = 4(1) - 1 = 4 - 1 = 3.
When x = 2, y = 4(2) - 1 = 8 - 1 = 7.
So we have the points (-2, -9), (-1, -5), (0, -1), (1, 3), and (2, 7).
Step 2: Plot the points on a coordinate plane.
(-2, -9)
(-1, -5)
(0, -1)
(1, 3)
(2, 7)
Step 3: Draw a line connecting the points.
Now we have the graph of the relation y = 4x - 1.
Next, we will apply the vertical line test. The vertical line test is used to determine if a graph represents a function. It states that if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
When we apply the vertical line test to the graph of the relation y = 4x - 1, we can see that for any vertical line we draw, it will intersect the graph at most once.
Therefore, based on the graph and the vertical line test, we can conclude that the relation y = 4x - 1 is a function.
Answer: 1
To determine whether the relation y = 4x - 1 is a function, we first need to graph it.
To graph the relation, we can assign values to x, calculate the corresponding y-values, and plot the points on a coordinate plane. Let's choose a few arbitrary x-values and find the corresponding y-values:
When x = 0, y = 4(0) - 1 = -1. So we have the point (0, -1).
When x = 1, y = 4(1) - 1 = 3. So we have the point (1, 3).
When x = -1, y = 4(-1) - 1 = -5. So we have the point (-1, -5).
Now, let's plot these points on a graph:
-5|
-4|
-3|
-2|
-1| ●(0,-1)
0|
1| ●(1,3)
2|
3|
4|
5|
Now that we have graphed the relation, we can apply the vertical line test.
The vertical line test states that if a vertical line drawn from any point on the graph intersects the graph more than once, then the relation is not a function. However, if a vertical line intersects the graph at most once for every x-value, then the relation is a function.
In our graph, we can see that for each x-value, there is only one corresponding y-value. Therefore, the vertical line test passes, and the relation y = 4x - 1 is a function.
Thus, the answer to the question is 1.