The function given:
[tex]f(x)=x^3-4x^2+7[/tex]We need the end behavior of the function.
The end behavior of a function describes what happens at the end of the x-axis.
In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
Let's graph the function. The graph is shown below:
As we can see,
• as we go towards infinity in the x direction, the function approaches infinity (y-direction).
,• as we go towards negative infinity in the x direction, the function approaches negative infinity (y-direction).
