Question

F(x) = x3 – 4x2 +7Find the end behavior of the function.

Answer 1

The function given:

`f(x)=x^3-4x^2+7`

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).