Question: 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.

I know 1 is the end point, but I'm not sure what else to do. Is there another end point and are the y coords included?

The endpoint at x=1 is a solid symbol

that at x=5 is open
Just the way you mark intervals on the number line.

Yes, the y-coordinates are included, since the endpoints lie on the graph.

To identify the end points of a graph with the given domain 1 ≤ x < 5, it is correct that one end point is x = 1. However, there is no other specific end point since the domain is open-ended on the right side (x < 5).

On the graph, x = 1 will be a single point represented by a dot. Since the domain includes 1 (1 ≤ x), the corresponding y-value is included in the range of the function.

On the right side, as the domain is open-ended, there is no specific x-value that serves as an end point. The graph will continue indefinitely towards positive x-values.

To describe the end points of the graph with the given domain 1≤x<5, we consider the two possible end values of x within this interval.

1. The lower end point: Since the domain states that x must be greater than or equal to 1, the lowest x-value within the interval is x = 1. This means that 1 is indeed an end point.

To determine what the end point looks like on the graph, we can imagine an open circle or an unfilled dot at x = 1 on the x-axis. This signifies that the graph approaches but does not include x = 1.

Regarding the y-values, we are unsure without further information about the function or graph itself. If the y-values corresponding to x = 1 are included in the range of the function, it would typically be represented by a filled dot or a closed circle on the graph. However, since you mentioned that the corresponding y-values are uncertain, we cannot determine if they are included or excluded from the range based solely on the given information.

2. The upper end point: The domain states that x should be less than 5, which means that the highest value for x within the interval is x = 5 - ε (where ε represents a very small positive number approaching zero). However, since ε is infinitesimal, we can only approach x = 5 but not actually reach it within this domain.

Similarly to the lower end point, the upper end point at x = 5 would also be represented by an open circle or an unfilled dot on the x-axis. Again, without additional information about the function or graph, we cannot determine if the corresponding y-values are included in the range.

Therefore, based on the given domain 1≤x<5, the graph has one end point at x = 1, and the status of the corresponding y-values within the range cannot be determined without more information.