To determine the domain of the graph that represents the ball’s height, \( h \), over time, \( t \), we need to consider the values that \( t \) (time) can take. The domain consists of all possible values of \( t \) for which the height \( h \) is defined.
Based on the description of the graph:
- The horizontal axis (time, \( t \)) is numbered from 1 to 4.
- There are points at \( t = 0 \), \( t = 1 \), and \( t = 3 \) with heights of \( h = 48 \), \( h = 64 \), and \( h = 0 \) respectively.
- There is a solid curved line connecting these points, indicating a continuous function describing the height of the ball over time.
Since the graph only specifies points between \( t = 0 \) and \( t = 3 \), and we are dealing with a continuous curve connecting these points, it implies that the entire range between these points is part of the domain.
Therefore, the domain of the function, which represents the ball’s height over time, is:
\[ t \in [0, 3] \]
In interval notation, this means the domain is:
\[ [0, 3] \]
This indicates that \( t \) can take any value from 0 to 3, inclusive.
A graph where the horizontal axis shows time (t), numbered 1 to 4, and the vertical axis shows height (h) numbered 10 to 60. Solid circles appear at point (0, 48), point (1, 64), point (3, 0). A solid curved line connects all 3 points.
Leon throws a ball off a cliff. The graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds.
What is the domain?
1 answer