Consider the function represented by the graph.
On a coordinate plane, a straight line with a negative slope begins on the y-axis at (0,9) and exits the plane at (8,1). What is the domain of this function?
The Correct Answer and Explanation is:
To determine the domain of the function represented by the described graph, we first need to understand what is meant by the “domain” of a function. The domain is the complete set of possible values of the independent variable (typically (x)) for which the function is defined. In this case, we have a straight line segment that starts at the point (0, 9) on the y-axis and ends at the point (8, 1).
Given the endpoints of the line segment, we can analyze the values of (x) that this function can take. The graph starts at (x = 0) and ends at (x = 8). This means that the function is defined for all (x) values in the interval starting from 0 up to 8, inclusive. There are no breaks, holes, or vertical asymptotes within this interval, as it is a continuous straight line segment.
Mathematically, we can express the domain of this function as an interval:
[
\text{Domain: } [0, 8]
]
This notation indicates that the function includes both endpoints, meaning the function takes on values at (x = 0) (where (y = 9)) and (x = 8) (where (y = 1)).
In summary, the domain of the function represented by the line segment is all real numbers (x) such that (0 \leq x \leq 8). It is crucial to understand that outside this interval, the function is not defined, as there are no corresponding (y) values on the graph for (x) values less than 0 or greater than 8. Therefore, when analyzing functions, it is important to look closely at the endpoints and any restrictions imposed by the graph to accurately define the domain.