When looking at a graph of a function, it can be difficult to determine what it represents. Fortunately, there is a helpful tool to help interpret the graph: a table. This article will explain how to use a table to describe the behavior of the graph of f(x) = 2×3 – 26x – 24.
Examining the Graph
The graph of f(x) = 2×3 – 26x – 24 is a cubic function that has a single real root. It is a downward-facing parabola with an x-intercept at (2, 0) and a y-intercept at (0, -24). The graph has a local minimum at (4, -32) and a local maximum at (-1, -7).
Analyzing the Table
The table below describes the behavior of the graph of f(x) = 2×3 – 26x – 24.
| x-values | y-values | Behavior of the Graph |
|---|---|---|
| x< -1 | y< -7 | Decreasing |
| -1 < x < 2 | y< 0 | Increasing |
| x> 2 | y> 0 | Decreasing |
The table shows that the graph is decreasing for x-values less than -1 and for x-values greater than 2. It is increasing for x-values between -1 and 2.
By examining the graph and analyzing the table, we can see that the graph of f(x) = 2×3 – 26x – 24 is a downward-facing parabola with a single real root. It has a local minimum at (4, -32) and a local maximum at (-1, -7). The table shows that the graph is decreasing for x-values less than -1 and for x-values greater than 2, and increasing for x-values between -1 and 2.
For those familiar with the study of basic mathematics, the question of which table describes the behavior of the graph of F(X) = 2×3 – 26x – 24 is one that is easily answered. In order to examine the behavior of the graph of F(X) = 2×3 – 26x – 24, one must first consider the shape of the graph.
The graph of F(X) = 2×3 – 26x – 24 is a parabola that is downward facing. This means that the graph starts at a relatively high point on the y-axis and then moves downwards gradually over the x-axis, eventually reaching a low point before returning to the starting position. From this, we can conclude that the graph displays an increasing trend when the x-value increases and a decreasing trend when the x-value decreases.
In order to understand the behavior of the graph in more detail, it is helpful to use a table to illustrate the graph’s changing values with respect to the changing x-values. This can be done by plotting the graphical values of the equation along the x-axis and the y-axis. In this case, the table would look something like this:
X-Value | Y-Value
———————–
-6 | 60
-2 | -4
0 | -24
2 | -20
6 | 24
From this table, we can see that the graph of F(X) = 2×3 – 26x – 24 begins with an initial value of -24 (Y-value) at point 0 (X-value) on the graph and increases until it reaches its maximum value of 24 (Y-value) at point 6 (X-value) before returning to its starting point of -24 (Y-value). This behavior is characteristic of the basic parabola shape and serves to illustrate the graph’s basic behavior.
In conclusion, the table describes the behavior of the graph of F(X) = 2×3 – 26x – 24 by plotting the graphical values of the equation along the x-axis and the y-axis and illustrating the graph’s basic parabolic behavior as it moves from a starting point of -24 (Y-value) to its maximum value of 24 (Y-value) and back again.
