Introduction
In mathematics, a function is a relation between two sets of values, usually denoted as a set of input values and a set of output values. One of the important aspects of a function is its vertex, which is the highest or lowest point in a graph, depending on the specific type of function. The size and position of a graph’s vertex can be important when studying the properties of a function. In this paper, we will discuss three statements about a function and determine whether or not each statement is true.
Statement 1: The vertex of the function is at (–4,–15).
The first statement being discussed is that the vertex of the function is at (–4,–15). This statement is true. By looking at the graph of the function, it can be seen that the vertex of the function is indeed located at the point (–4,–15). At this point, the graph reaches its highest or lowest point.
Statement 2: The vertex of the function is at (–3,–16).
The second statement being discussed is that the vertex of the function is at (–3,–16). Unfortunately, this statement is false. By looking at the graph of the function, it can be seen that the vertex of the function is actually located at (–4,–15). The vertex is not located at (–3,–16).
Statement 3: The graph is increasing on the interval x > –3.
The third statement being discussed is that the graph is increasing on the interval x > –3. This statement is true. By looking at the graph, it can be seen that the graph is indeed increasing on the interval x > –3. On this interval, the y-values increase as the x-values increase.
Statement 4: The graph is positive only on the intervals where x < –7 and where x > 1.
The fourth statement being discussed is that the graph is positive only on the intervals where x < –7 and where x > 1. This statement is true. By looking at the graph, it can be seen that the graph is positive only on the intervals where x < –7 and where x > 1. On these intervals, the y-values are greater than 0.
Statement 5: The graph is negative on the interval x < –4.
The fifth statement being discussed is that the graph is negative on the interval x < –4. This statement is also true. By looking at the graph, it can be seen that the graph is indeed negative on the interval x < –4. On this interval, the y-values are less than 0.
Conclusion
In this paper, we discussed three statements about a function and determined whether or not each statement was true. We found that the first statement, that the vertex of the function is at (–4,–15), is true. We also found that the second statement, that the vertex of the function is at (–3,–16), is false. Furthermore, we found that the third, fourth, and fifth statements, that the graph is increasing on the interval x > –3, that the graph is positive only on the intervals where x < –7 and where x > 1, and that the graph is negative on the interval x < –4, respectively, are all true.