A graph has the domain 1≤x<5
. Describe the end points of the graph. Include where the end points are, what they look like on the graph, and if the corresponding y-values are included in the range of the function.(2 points)
The graph has two end points: one at x = 1 and the other at x = 5.
At x = 1, the end point appears as a dot or a point on the graph. The y-value at this end point may or may not be included in the range of the function, depending on the specific function or equation.
At x = 5, the end point appears as a dot or a point on the graph. Similar to the previous end point, the y-value at this end point may or may not be included in the range of the function depending on the specific function or equation.
The given domain of the graph is 1≤x<5. This means that the graph covers all values of x that are between or equal to 1, but less than 5.
Let's describe the end points of the graph:
1. The left endpoint is x = 1. On the graph, this point is a solid dot or a closed circle located at x = 1. Since the domain includes the value 1, the corresponding y-value may or may not be included in the range of the function.
2. The right endpoint is x = 5. On the graph, this point is an open circle located at x = 5. The domain specifies that x should be less than 5, so 5 itself is not included. Therefore, the corresponding y-value at x = 5 is not included in the range of the function.
To describe the end points of the graph, we need to understand what it means for the domain to be 1≤x<5. This notation indicates that the graph includes all values of x greater than or equal to 1, but less than 5. In other words, the graph only includes x-values between 1 and 5, excluding both endpoints.
Since the graph does not extend beyond the given domain, we have two end points to consider. The first end point occurs at x = 1, and the second end point occurs at x = 5.
1. End point at x = 1:
At x = 1, the graph of the function comes to a stop. On the graph, the point would be represented by a closed circle or dot at the corresponding x-value (1) on the x-axis. However, since the domain is "1≤x<5" and excludes the endpoint 1, the dot should not be filled in. This indicates that the function does not include the corresponding y-value for x = 1 in its range.
2. End point at x = 5:
At x = 5, the graph once again comes to a halt. Similar to the first end point, a closed circle or dot should be placed at the x-value (5) on the x-axis to represent this point. However, since the domain is "1≤x<5" and excludes the endpoint 5, the dot should also be unfilled. This means that the function does not include the corresponding y-value for x = 5 in its range.
In summary, the end points of the graph are represented by unfilled dots on the graph at x = 1 and x = 5. The corresponding y-values for these end points are not included in the range of the function due to the exclusions in the domain.